{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "79FAC74C4D88446C85DB130914CD918F",
    "jupyter": {},
    "notebookId": "654741f6d74b63fed5dd17ca",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    " # <center> Lecture7 : Posterior Inference &  Estimation  </center>  \n",
    " \n",
    " ## <center> Instructor: Dr. Hu Chuan-Peng  </center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在第六课中，我们已经介绍了 PyMC 的基本用法。\n",
    "- 其实，PyMC 就是一种 概率编程语言（PPL）框架，它帮助我们在 Python 中进行贝叶斯模型的构建和后验推断。\n",
    "- 通过 PyMC，我们可以定义先验分布、设置似然函数、运行采样算法，并在采样后对模型结果进行可视化和诊断。\n",
    "- PyMC 支持多种采样方法，如 MCMC（马尔可夫链蒙特卡洛），这使得 PyMC 在保持高效性的同时，能够处理更复杂的模型，满足多种统计建模需求。\n",
    "- PyMC 只是 PPL 框架的一个代表，不同的 PPL 框架（如 Stan）在设计和功能上各有特色。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 什么是概率编程语言（PPL，probabilistic programming language）\n",
    "\n",
    "概率编程语言的关键在于自动进行概率分布（尤其是贝叶斯后验分布）的推理过程。\n",
    "\n",
    "传统贝叶斯后验分布的推理过程中，我们需要定义先验，确定似然函数，然后使用 MCMC 等方法来计算后验分布。\n",
    "\n",
    "```python\n",
    "N = 10; Y = 9\n",
    "x = np.linspace(0, 1, 10000)\n",
    "pi = st.beta.pdf(x, alpha=2, beta=2)\n",
    "likelihood = st.binom.pmf(Y, N, x)\n",
    "\n",
    "posterior_unstandardized = likelihood * pi\n",
    "# then we need MCMC to get the posterior distribution\n",
    "# each iteration we will calculate posterior_unstandardized = likelihood * pi\n",
    "mh_simulation = mh_tour(N=5000) \n",
    "```\n",
    "\n",
    "\n",
    "对于概率编程语言，我们只需要定义先验和数据模型，然后就可以自动推断出后验分布。\n",
    "\n",
    "```python\n",
    "N = 10; Y = 9\n",
    "with pm.Model() as bb_model:\n",
    "    pi = pm.Beta('pi', alpha=2, beta=2)\n",
    "    likelihood = pm.Binomial('likelihood', n=N, p=pi, observed=Y)\n",
    "    trace = pm.sample(draws=5000)\n",
    "```\n",
    "\n",
    "可见，我们只需要在 PyMC 中定义似然函数模型 `likelihood` 之后使用 `pm.sample(draws=5000)` 就可以自动计算出后验分布, 而无需考虑如何使用 MCMC 等方法来计算后验分布。\n",
    "- 其中  `likelihood = pm.Binomial('likelihood', n=N, p=pi, observed=Y)` 相等于公式 $likelihood = \\text{Binomial}(\\text{N}, \\text{Y} | \\pi)$。\n",
    "\n",
    "<div style=\"padding-bottom: 30px;\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "PPL 框架还提供了其他更多的功能和特点，我们将在之后的课程中慢慢接触到：\n",
    "\n",
    "\n",
    "| 功能           | 描述                                                          | 主要用途                      |\n",
    "|-------------------------|---------------------------------------------------------------------------------------|--------------------------------------------------------|\n",
    "| **模型定义**            | 用简洁语法定义先验分布和似然函数，支持分层模型   | 简化模型构建流程，灵活定义复杂结构        |\n",
    "| **自动采样**            | 提供 MCMC (HMC、NUTS)、变分推断等多种近似算法     | 高效获取后验样本，适应高维复杂模型           |\n",
    "| **自动微分**            | 自动计算梯度，支持高维复杂模型                | 加速模型优化，适应复杂计算需求                    |\n",
    "| **诊断与调试**          | 提供 Trace Plot、R-hat 等诊断工具，检测采样质量与收敛性       | 确保采样结果可靠，识别采样问题                |\n",
    "| **后验分析和可视化**    | 提供后验分布图、密度图、置信区间等可视化工具     | 直观理解参数分布和不确定性，辅助决策             |\n",
    "| **后验预测**            | 从后验分布生成新观测数据，用于模型验证       | 检查模型合理性，评估预测效果               |\n",
    "| **灵活建模扩展性**      | 支持模块化建模、集成外部工具，构建自定义模型        | 适应不同应用场景，增强模型的扩展性         |\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 贝叶斯概率编程中的核心术语\n",
    "\n",
    "这些术语在贝叶斯统计和概率编程中具有重要应用。除了已经讲过的部分概念外，本节课将涉及一些新概念：\n",
    "\n",
    "\n",
    "| 术语（中英文全称）                                     | 定义                                                                                  |\n",
    "| --------------------------------------------- | ----------------------------------------------------------------------------------- |\n",
    "| 先验分布（Prior Distribution）                      | 先验分布是指在观察数据之前，研究人员对模型中未知参数的初始信念。这种信念可以基于现有研究或试点数据形成。                                |\n",
    "| 似然函数（Likelihood Function）                     | 似然函数是指特定参数下观测数据的概率，它是统计模型中选择参数的概率函数。例如，伯努利函数是描述硬币投掷统计的似然函数。                         |\n",
    "| 后验分布（Posterior Distribution）                  | 后验分布是指在观察到数据后，根据贝叶斯规则平衡先验知识与观测数据，对参数的更新信念。                                          |\n",
    "| 马尔可夫链蒙特卡洛方法（Markov Chain Monte Carlo, MCMC）   | MCMC是一种通过模拟来推断后验分布的采样方法。通过算法构建多个马尔可夫链，使得它们的平稳分布与感兴趣的后验分布相匹配，这个过程称为MCMC收敛。           |\n",
    "| 有效样本大小（Effective Sample Size, ESS）            | 有效样本大小是指与N个自相关样本具有相同估计力的独立样本数量。ESS常用于判断MCMC链中的抽样数量是否足以保证可靠的估计不确定性。                  |\n",
    "| Gelman-Rubin统计量（Gelman-Rubin Statistics, R̂）  | Gelman-Rubin统计量是链内变异性与链间变异性的比率。所有参数和感兴趣量接近1.0的值表明马尔可夫链蒙特卡洛算法已足够收敛到平稳分布。             |\n",
    "| 最高密度区间（Highest Density Interval, HDI）         | 最高密度区间是贝叶斯统计中参数可信范围的估计。它包括后验分布中的一个区间，该区间内的每个点的密度都高于区间外的点。                           |\n",
    "| 实践等效区间（Region of Practical Equivalence, ROPE） | 实践等效区间是预先定义的参数值范围，这些值被认为在实践上等同于零。用于判断参数估计是否显著不同于零。                                  |\n",
    "| 贝叶斯因子（Bayes Factor, BF）                       | 贝叶斯因子量化了一个统计模型相对于另一个模型的证据强度。大于1的值表明相对于原始模型，替代模型得到了更多的支持。                            |\n",
    "| 采样样本（Samples/Draws）                           | 采样样本值是指从后验分布中抽取的参数值，用作后验分布的近似，并通过蒙特卡洛积分获得后验分布的经验估计和感兴趣的汇总统计量。其采样结果在计算机术语中也称为 trace。 |\n",
    "| 调试样本（Tune）                                    | 调试样本是指在MCMC抽样过程中用于达到平稳分布的初始阶段，此阶段的样本通常被丢弃，不在最终分析中使用。也叫做 Warmup 活 burn-in，燃烧样本。      |\n",
    "| 链（Chains）                                     | 链是指来自单个MCMC链的一系列样本（或抽样值）。链用于诊断收敛性以及程序在特定应用中的其他潜在问题。                                 |\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9B1ED8438D2B4A1E93027F0BB775888B",
    "jupyter": {},
    "notebookId": "654741f6d74b63fed5dd17ca",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## 使用后验分布进行统计推断  \n",
    "\n",
    "我们已经知道可以凭借 PyMC 等方法来得到后验，但更具体的后验能告诉我们什么呢？  \n",
    "\n",
    "⭐这节课我们关注对 PyMC 等概率编程语言(PPL) 的输出结果进行分析，包括：\n",
    "\n",
    "* MCMC诊断\n",
    "* 后验估计  \n",
    "* 假设检验  \n",
    "\n",
    "\n",
    "\n",
    "<p align=\"center\">\n",
    "  <img src=\"https://cdn.kesci.com/upload/sm7veon5ei.png?imageView2/0/w/720/h/960\" alt=\"Image Name\">\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### A Beta-Binomial example in PyMC \n",
    "\n",
    "我们依旧以随机点运动任务为例，其中每个试验中参与者判断正确的概率用 $\\pi$ 表示。\n",
    "\n",
    "**模型假设**\n",
    "\n",
    "- 我们假设参与者判断正确的概率 $\\pi$ 是从 **Beta 分布**中抽样的：\n",
    "\n",
    "$$  \n",
    "\\begin{equation}  \n",
    "\\pi \\sim \\text{Beta}(\\alpha, \\beta)  \n",
    "\\end{equation}  \n",
    "$$  \n",
    "\n",
    "- 在每次试验中，参与者的成功次数 $Y$ 服从 **Binomial 分布**：\n",
    "\n",
    "$$  \n",
    "\\begin{equation}  \n",
    "Y \\sim \\text{Binomial}(n, \\pi)  \n",
    "\\end{equation}  \n",
    "$$  \n",
    "\n",
    "其中，$n$是试验的总次数，$Y$是成功次数。\n",
    "\n",
    "**模型设定**\n",
    "\n",
    "在这个例子中，我们可以使用Beta-Binomial 模型来表示：\n",
    "\n",
    "> 总试验数为N=10，成功次数为9 $(Y = 9)$  \n",
    "> 先验分布为：$\\pi    \\sim \\text{Beta}(2, 2)$  \n",
    "> 似然函数为：$Y|\\pi  \\sim \\text{Bin}(N, \\pi)$  \n",
    "\n",
    "对应的 PyMC 代码为：\n",
    "```python\n",
    "N = 10; Y = 9\n",
    "with pm.Model() as bb_model:\n",
    "    pi = pm.Beta('pi', alpha=2, beta=2)\n",
    "    likelihood = pm.Binomial('likelihood', n=N, p=pi, observed=Y)\n",
    "```\n",
    "\n",
    "<div style=\"padding-bottom: 30px;\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 对马尔科夫链的诊断 (Markov chain diagnostics) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "当我们定义好 PyMC 模型后，就可以使用 `pm.sample()` 函数进行采样。\n",
    "\n",
    "`trace`包含了所有参数的采样结果，即参数的后验分布的采样。\n",
    "\n",
    "```python\n",
    "with bb_model:\n",
    "    trace = pm.sample(draws=5000)\n",
    "```\n",
    "\n",
    "但使用这些采样结果前，我们需要回答一个问题：这些采样结果是否可信？🤔"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "由于这些采样来自于 MCMC 算法，即马尔科夫链蒙特卡洛算法，而模拟采样方法的关键是 \"近似 \"和 \"收敛\"  。\n",
    "\n",
    "这就引出了以下问题：  \n",
    "\n",
    "- 好的马尔可夫链是什么样的？  \n",
    "- 如何判断马尔可夫链样本是否产生了合理的后验近似值？  \n",
    "- 马尔可夫链样本量应该多大？  \n",
    "\n",
    "诊断的意义：确定好的trace的标准，为我们不知道真实的后验时作为标准进行推断。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在本节中，我们将重点介绍几种诊断方法：\n",
    "\n",
    "- 可视化诊断：轨迹图 (trace plot)和平行链 (parallel chains)。  \n",
    "- 量化诊断指标：有效样本大小 ESS(effective sample size)、自相关性 (autocorrelation)和 $\\hat{R}$ (R-hat)。  \n",
    "    \n",
    "> 这些诊断方法的使用应综合考虑。没有一种视觉或数值诊断方法是万能的，通常要一起考虑。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### trace plots  \n",
    "\n",
    "轨迹图 (trace plot) 是一种可视化方法，用于显示马尔可夫链的轨迹，即马尔可夫链在参数空间中的位置。  \n",
    "- 图中的横坐标是时间步长，纵坐标是参数的值。  \n",
    "- 轨迹图往往结合参数的后验分布一起展示，以便于观察采样样本对于参数分布的代表性。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们先来看一下正常的轨迹图是什么样：  \n",
    "\n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/s2le92xkaq.png?imageView2/0/w/500/h/500)  \n",
    "\n",
    "- 这是之前 Beta-Binomial model 的示例。  \n",
    "- 上图：轨迹图看起来像一堆白噪声，没有明显的趋势或现象，这意味着**链是稳定的**。  \n",
    "- 下右：展示了正常的参数后验分布的情况。\n",
    "\n",
    "<div style=\"padding-bottom: 30px;\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "一个糟糕的轨迹图可能看起来像这。显然这种条件下的后验参数分布在用于后续推断时是必须非常谨慎的：  \n",
    "\n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/s2le9nbz6q.png?imageView2/0/w/450/h/450)  \n",
    "\n",
    "图中上部分链 A：  \n",
    "\n",
    "- 链 A 中的轨迹图显示，它在 5000 次迭代后还没有稳定下来，并且它只探索了 0.6 到 0.9 之间的参数值。  \n",
    "  - 下降趋势也暗示着链值之间存在着很强的相关性--它们看起来并不像独立的噪音。  \n",
    "  - 虽然马尔可夫链本身具有依赖性，但它们越像噪声(独立样本的表现)，得出的后验近似值误差就越小（粗略地说）。  \n",
    "- 结合后验分布图：**它的后验近似值高估了真实分布中央部分，而完全低估了这个范围之外值的可信度**。  \n",
    "\n",
    "图中下部分链 B：   \n",
    "- 链 B 表现出不同的问题，迹线图中的部分区域存在**两条完全·平直的线**所显示的那样，  \n",
    "  - 这意味着，**当它采样到较小的参数值时，往往会陷入这个值的附近，** 这也表明了一种局部的高相关性。  \n",
    "  - 链条 B 在陷入困境时，会对后验参数左侧尾部的值进行**过度采样**。         \n",
    "- 结合密度图  \n",
    "  - 虽然链 B 后验分布和真实分布的重合性更好，但它存在多峰分布，原因在于过度采样。\n",
    "\n",
    "<div style=\"padding-bottom: 30px;\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果我们得到一个糟糕的轨迹图，如何进行补救📍：  \n",
    "\n",
    "- 1. 检查模型。确定假定的**先验模型**和**数据模型**是否合适？    \n",
    "- 2. 对数据链进行**更多迭代**。一些不理想的短期连锁趋势可能会在长期内得到改善。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 有效样本大小 ESS(effective sample size)和自相关性 (autocorrelation)  \n",
    "\n",
    "MCMC 链的样本存在相关性，如本身的特性一样，后一个参数的采样过程与前一个参数有关，这导致间隔一个位置的参数样本间的相关性很高。  \n",
    "\n",
    "然而，MCMC 链又要求“无记忆性”，即样本之间最好是独立的。  \n",
    "\n",
    "🤔那么如何理解 MCMC链中独立与相关的矛盾？  \n",
    "- 需要清楚的是，相关性仅限于间隔一个位置的参数样本。  \n",
    "- 而独立性的要求是针对于参数样本间大于一个间隔的情况的。  \n",
    "\n",
    "自相关就可以很好的描述样本之间的相关性；而有效样本量针对于描述样本的独立性。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**自相关性 (autocorrelation)**  \n",
    "\n",
    "- 可用于评估马尔科夫链的样本之间的相关性。  \n",
    "- 强烈的自相关性或依赖性是一件坏事--它**与较小的有效样本比相伴而生**，说明我们得出的后验近似值可能不可靠。  \n",
    "    \n",
    "根据马尔可夫链的简单构造，链值之间必然存在一些自相关性--一个链值($\\pi_{i}$)取决于前一个链值（$\\pi_{i-1}$），而前一个链值（$\\pi_{i-1}$）又取决于前一个链值（$\\pi_{i-2}$），依此类推。**这种依赖链还意味着，每个链值都在一定程度上依赖于之前的所有链值**。  \n",
    "\n",
    "- 例如，$\\pi_{i}$ 取决于$\\pi_{i-1}$，而$\\pi_{i-1}$ 取决于$\\pi_{i-2}$，因此$\\pi_{i}$ 也取决于$\\pi_{i-2}$。  \n",
    "- 然而，**这种依赖性或自相关性会逐渐消失**。  \n",
    "    \n",
    "> 这就像托布勒的地理学第一定律：万事万物都与其他事物相关，**但近处的事物比远处的事物更相关**。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "一个自相关良好的例子：  \n",
    "\n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/s2lefvdivs.png?imageView2/0/w/640/h/640)  \n",
    "\n",
    "- 图左是之前提到的轨迹图(trace plot)。  \n",
    "- 右图是自相关图，x轴是样本之间的间隔距离，y 轴为自相关性。  \n",
    "- 例如 0 代表所有参数采样和自己的相关性 (这显然为1)，1代表所有参数和间隔一个距离参数的样本的相关性，该相关性依然很高，大约为 0.5，表明相差仅 1 步的链值之间存在中等程度的相关性。随后自相关性迅速下降，到间隔 5 个样本时相关性下降为 0。  \n",
    "- 也就是说，相差间隔越大，马尔科夫链值之间的相关性越小，这是一个好消息，表明马尔科夫链正在**快速混合**，即在后验可信 π 值范围内快速移动，从而至少模拟了一个独立样本。  \n",
    "- 对于间隔解释的例子：如果有100个参数形成的样本，编号为 1-100。 那么间隔10，就代表，10-100组成的样本。为了让 10-100 和原始的样本长度相同，我们可以使用 1-90和 10-100 的样本进行相关分析。需要注意的是，存在更好的数学方法可以避免间隔越大，样本量越小的问题。扩展阅读: https://zhuanlan.zhihu.com/p/77072803  \n",
    "  \n",
    "<div style=\"padding-bottom: 30px;\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "一个自相关糟糕的例子：  \n",
    "\n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/s2lew3t7qx.png?imageView2/0/w/640/h/640)  \n",
    "- 自相关曲线的缓慢下降表明，链值之间的依赖关系不会很快消失。  \n",
    "- 相差整整 20 步的马尔可夫链值之间存在大约 0.9 的相关性！  \n",
    "- 由于其链值与前值的联系非常紧密，因此该链的**混合速度很慢**，**需要很长时间才能充分探索后验的全部范围**。  \n",
    "- 因此，我们应该谨慎使用该链来近似后验。  \n",
    "\n",
    "<div style=\"padding-bottom: 30px;\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**重要概念：Fast vs slow mixing Markov chains**  \n",
    "\n",
    "- 快速混合：指链表现出与独立样本的行为，即混合链值之间的自相关性迅速下降，有效样本大小比相当大。  \n",
    "    \n",
    "- 慢速混合：指链不具有独立样本的特征，即混合链值之间的自相关性下降非常缓慢，有效样本大小比很小。换句话说，链在后验可信值范围内 \"缓慢 \"移动。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果我们的链混合速度太慢该怎么办呢？一些推荐的策略📍：  \n",
    "\n",
    "- 第一， \"运行更长的链\"。如果迭代次数足够多，即使是缓慢的混合链最终也能产生良好的后验近似值。  \n",
    "    \n",
    "- 第二，使得马尔科夫链更薄。  \n",
    "    \n",
    "    - 例如，在包含 5000 个样本的链中，我们每间隔一个参数来保留样本，并丢弃其余的样本，例如：{$\\pi_{2}$, $\\pi_{4}$, ..., $\\pi_{5000}$}.  \n",
    "        \n",
    "    - 甚至，我们可以每间隔十样本来保留样本：{$\\pi_{10}$, $\\pi_{20}$, ..., $\\pi_{5000}$}.  \n",
    "        \n",
    "- 通过舍弃中间的抽样，我们可以消除低间隔带来的强相关性。  \n",
    "    \n",
    "    - 还记得吗，$\\pi_{20}$与稀疏链中的前一个值 ($\\pi_{10}$)的相关性小于与原始链中的前一个值 ($\\pi_{19}$)的相关性。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**一个使 MCMC 链变得更薄(thin)来减少自相关的示例：**  \n",
    "\n",
    "我们使用 thin=10 来使得链变得比之前薄10倍，也就是从5000个样本中，每隔10个样本宝保留一个，总共500个样本将被保留。  \n",
    "\n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/s2lew3t7qx.png?imageView2/0/w/640/h/640)  \n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/s2lf7kf4e8.png?imageView2/0/w/640/h/640)  \n",
    "\n",
    "- 上图为之前没有变薄的MCMC链。下图为变薄了10倍的链。  \n",
    "- 可以看到，自相关性产生了快速的下降。  \n",
    "- 但是，这可能任然无法完全消除自相关性。  \n",
    "\n",
    "🤔一个值得思考的问题：  \n",
    "\n",
    "- 使用 thin=10 时，我们可用的样本变得更少，是否值得损失 90% 的原始样本值呢？\n",
    "<div style=\"padding-bottom: 30px;\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "**有效样本量比率 Effective sample size ratio**  \n",
    "\n",
    "为了避免链中相关性的影响，有效样本量 (effective sample size)被提出，以用于描述链中独立样本的数量。因为根据 MCMC 的特性，我们需要链存在无记忆性，也就是大于两个间隔的参数样本间不存在或者存在很小的相关性。有效样本量计算了这些不存在或者存在很小的相关性样本的数量。  \n",
    "\n",
    "$\\frac{N_{neff}}{N}$  \n",
    "\n",
    "- N 表示依赖马尔可夫链的实际样本量或长度。  \n",
    "- $N_{eff}$ 为马尔可夫链的有效样本大小，量化了产生等效精确后验近似所需的独立样本数量。  \n",
    "- $N_{eff}$ 越大越好，但马尔可夫链近似的准确性通常只能达到较小独立样本的准确性。也就是说，  \n",
    "- 通常情况下，$N_{eff}$ < N，因此有效样本大小比小于1。我们往往会对有效样本量比小于 0.1 的马尔可夫链产生怀疑，即 Neff/N < 10%。  \n",
    "\n",
    "假设马尔科夫链的长度为 20,000，并且包括 6800 个独立样本，即有效样本量 ESS = 6800。  \n",
    "- 因此，有效样本量比率 EFF=34%，代表相当于我们只使用了 34% 的独立样本。  \n",
    "- 由于这个比例高于 0.1，这是是可以接受的。并且 ESS > 400。  \n",
    "  \n",
    "> 更详细的定义请参见 Vehtari 等人（2021）。如需了解有效样本量, R-hat等指标的的联系，请参阅 Vats 和 Knudson (2018)。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**补充，如何计算ESS**  \n",
    "\n",
    "\n",
    "ESS表示与独立和均匀采样相当的有效样本数量，可以使用以下公式计算：  \n",
    "\n",
    "ESS = $N / \\tau$  \n",
    "\n",
    "- 其中，N是总的采样数量。  \n",
    "- $\\tau$为自相关时间。  \n",
    "\n",
    "估计自相关时间（Autocorrelation Time，$\\tau$）：自相关时间表示样本之间的相关性消失所需的步数。它可以通过截尾自相关函数进行估计。\n",
    "自相关时间$\\tau$可以通过求和截尾自相关函数的面积来估计，可以使用以下公式计算：  \n",
    "\n",
    "$\\tau = 1 + 2 * \\sum{(TACF(lag))}$\n",
    "\n",
    "- 其中，lag表示滞后的范围。  \n",
    "\n",
    "\n",
    "计算自相关函数（Autocorrelation Function，ACF）：  \n",
    "- 首先，计算采样序列中不同滞后（lag）的自相关系数。  \n",
    "- 滞后为0时，自相关系数等于1；滞后为1时，自相关系数表示第一个样本与第二个样本之间的相关性；以此类推。  \n",
    "- 自相关函数的计算可以使用统计软件或编程语言中的相关函数。  \n",
    "\n",
    "计算截尾自相关函数（Truncated Autocorrelation Function，TACF）：  \n",
    "- 为了避免计算无限滞后的自相关系数，通常会截取滞后一定范围内的自相关系数。  \n",
    "- 选择一个合适的截断范围，例如滞后至自相关系数小于0.1，可以避免过多计算。  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### R-hat and comparing parallel chains  \n",
    "\n",
    "自相关和有效样本量仅针对于描述一条MCMC链的有效性。假如我们获得了四条并行的马尔可夫链。我们不仅希望看到每条链的稳定性，还希望看到**四条链的一致性**。  \n",
    "\n",
    "可以想象，如果四条链的结果并不一致，那么推断结果的可靠性就很难保证。  \n",
    "\n",
    "同样，我们首先展示一个良好的并行链的结果：  \n",
    "\n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/s2lg1juesc.png?imageView2/0/w/640/h/640)  \n",
    "\n",
    "- 四条链产生的后验近似值几乎没有差别，这证明我们的模拟是稳定的。\n",
    "\n",
    "<div style=\"padding-bottom: 30px;\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "为了便于比较和展示一个糟糕的并行链的结果，我们用更短的马尔可夫链模拟来演示。  \n",
    "\n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/s2lfz6esan.png?imageView2/0/w/640/h/640)  \n",
    "\n",
    "- 运行四条并行链仅进行 100 次迭代，其中 50 次为warmup (见之前的词典解释)，因此最终产生 50 * 100 个样本量。\n",
    "\n",
    "- 虽然这些链的轨迹图表现出相似的随机行为，但它们对应的密度图却不尽相同，因此产生的后验近似值也不尽相同。  \n",
    "\n",
    "这表明，如果我们只进行了 100 次迭代就停止模拟，那结果是不稳的。\n",
    "\n",
    "<div style=\"padding-bottom: 20px;\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "此外，不同链样本之间的变异性的一致性非常重要。  \n",
    "\n",
    "之前的结果同样显示，其中四条链具有相似的变异：  \n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/s2lg1juesc.png?imageView2/0/w/640/h/640)  \n",
    "\n",
    "\n",
    "- 中图显示，四条链的可变性几乎是相同的。  \n",
    "- 因此，右图中，所有链的变异与综合为单个链的变异性相似。\n",
    "\n",
    "<div style=\"padding-bottom: 10px;\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "一个糟糕的例子：  \n",
    "\n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/s2lg5bgzbr.png?imageView2/0/w/640/h/640)  \n",
    "\n",
    "\n",
    "- 四条平行链产生了相互冲突的后验近似值（中图）  \n",
    "- 当我们将这些链组合在一起时，后验近似值不稳定且较差（右图）。  \n",
    "- 因此，所有链中参数值的范围和变异性远大于任何单个链中参数值的范围和变异性。\n",
    "\n",
    "<div style=\"padding-bottom: 10px;\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们可以直观地看出，所有链条上的数值变化与单个并行链条内部的数值变化之间的关系非常重要。具体来说  \n",
    "\n",
    "- 在 \"好的 \"马尔可夫链模拟中，所有并行链的变异性总和将与任何单个链内的变异性**大致相当**；  \n",
    "- 在 \"坏的 \"马尔可夫链模拟中，所有并行链的变异性总和可能**超过**每个链内的典型变异性  \n",
    "    \n",
    "我们可以使用 $\\hat{R}$ 量化综合链变异性和链内变异性之间的关系。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\hat{R}$ 指标（称 \"R-hat\"）为并行链的可视化比较提供了具体的数学指标。  \n",
    "\n",
    "\n",
    "$$  \n",
    "\\hat{R} = \\frac{V_{combined}}{V_{within}}  \n",
    "$$  \n",
    "- $\\hat{R}$ 通过比较所有链上采样值的变异性和每个单独链上的变异性来解决一致性问题。  \n",
    "- combined 代表所有链的样本值的总变异。  \n",
    "- within 代表每个链内部样本值的变异。  \n",
    "\n",
    "理想情况下，$\\hat{R}$ ≈ 1，反映了平行链的稳定性。  \n",
    "- 相反，$\\hat{R}$ > 1表示链之间的变异不稳定，即组合链内的变异性大于单个链内的变异性。  \n",
    "- 虽然不存在黄金法则，但$\\hat{R}$比率大于1.05会给模拟的稳定性带来危险信号。  \n",
    "\n",
    "> 更详细的定义请参见 Vehtari 等人（2021）。如需了解有效样本量, R-hat等指标的的联系，请参阅 Vats 和 Knudson (2018)。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对于示例1  \n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/s2lg1juesc.png?imageView2/0/w/640/h/640)  \n",
    "- $\\hat{R}$ 值等于 1，这反映了四个并行链之间和链内部的变异性存在很好的一致性。  \n",
    "\n",
    "对于示例2  \n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/s2lg5bgzbr.png?imageView2/0/w/640/h/640)  \n",
    "\n",
    "- $\\hat{R}$ = 5.35，这表明所有链值的方差总和是每个链内典型方差的 5 倍多。这远远超过了 1.05 的标准，充分证明假设平行链并没有产生一致的后验近似值。  \n",
    "- 因此 MCMC 的模拟近似是不稳定的。其后验分布的结果不可用于后续推断。\n",
    "\n",
    "<div style=\"padding-bottom: 30px;\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 代码演示 -- MCMC 诊断\n",
    "\n",
    "使用 PyMC 建模的模型默认使用 MCMC 方法进行参数估计。  \n",
    "\n",
    "并且我们可以很方便的使用 `arviz` 对MCMC进行可视化和基于数学化标准的诊断"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "首先，我们建立一个简单的 beta 模型，并对该模型使用MCMC采样方法 (以下术语可见课件上分术语表) \n",
    "- 设置采样样本数 (draws) 为 5000  \n",
    "- 设置 MCMC 链 (chains) 的数量为 4，和上面的示例一样。  \n",
    "- 设置 MCMC 调试样本的数量 (tune) 为0，而默认 tune 为 1000。  \n",
    "    - 这里暂时理解 tune 为提前进行 MCMC 采样 1000次，然后丢弃掉这些采样。  \n",
    "    - 根据 MCMC 的性质，链中越早的采样越不稳定。因此，丢掉这些采样可以保证后续的采样更加稳定。  \n",
    "    - 后续课程会详细介绍该参数的意义。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [pi]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3aeb7fd9dbc64b03a3072dd112cde44b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 0 tune and 5_000 draw iterations (0 + 20_000 draws total) took 2 seconds.\n"
     ]
    }
   ],
   "source": [
    "import pymc as pm\n",
    "import arviz as az\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 设置数据\n",
    "N = 10; Y = 9\n",
    "# 创建PyMC模型\n",
    "bb_model = pm.Model()\n",
    "\n",
    "with bb_model:\n",
    "    pi = pm.Beta('pi', alpha=2, beta=2)\n",
    "    likelihood = pm.Binomial('likelihood', n=N, p=pi, observed=Y)\n",
    "\n",
    "#采样过程仍在该容器中进行\n",
    "with bb_model:\n",
    "    trace = pm.sample(draws=5000,                   # 设置MCMC采样样本的数量\n",
    "                      tune=0,                       # 设置调试样本的数量\n",
    "                      chains=4,                     # 设置4条MCMC链\n",
    "                      random_seed=84735)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "绘制 trace 图。  \n",
    "\n",
    "- 可以看到，每条链的后验分布都重合在一起。  \n",
    "- MCMC链的行为表现得类似噪音一样，这是一个好的表现。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = az.plot_trace(trace, legend = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "绘制自相关图  \n",
    "\n",
    "- 可以看到，随着间隔的下降，自相关也快速下降"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAl8AAAG8CAYAAADgh8CsAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8pXeV/AAAACXBIWXMAAA9hAAAPYQGoP6dpAAA8kklEQVR4nO3df1xUdaL/8fcgMSjBhI0lpuhaEGk/rPxKmQbkIma/rK3UqITU1h7VrrWWi1lIdrOtR7e95XXtaiqba2nlrXvF/FE6KqbkXjcz0yIVRdMS04GFHETO948eMyvya4YfH0Bez8djHo/4nM/5/HgcZ+bdOWc+x2ZZliUAAAAYEdTSAwAAAGhPCF8AAAAGEb4AAAAMInwBAAAYRPgCAAAwiPAFAABgEOELAADAIMIXAACAQYQvAAAAgwhfABCAxMRE2Ww2uVyulh4KgDaK8AUAAGAQ4QsAAhAdHa1LL71UnTp1aumhAGijbDxYGwAAwBzOfAEAABhE+ALQLtlsNtlsNknSokWLNGDAAJ177rnq3LmzRowYoa+++qrG/bjhHkBjEb4AtGsvv/yyUlNTVVhYqMsuu0wVFRX66KOPNGDAAOXm5rb08ACchQhfANq1qVOn6tVXX9XBgwe1ZcsWHT58WKmpqfr55591//336+eff27pIQI4yxC+ALRrN998s5588kkFBf3ycdipUyfNmzdPXbt21b59+/Tuu++28AgBnG0IXwDatUcffbRaWUhIiMaNGydJWrlypekhATjLEb4AtGuXXXZZneXffvutyeEAaAcIXwDatQsuuKDG8gsvvFCSVFJSYnI4ANoBwheAdu3IkSM1lv/444+SpPDwcJPDAdAOEL4AtGs7d+6sszw2NtbkcAC0A4QvAO3arFmzqpWVl5frrbfekiQNHTrU9JAAnOUIXwDatZycHP3Hf/yHvI+5/fnnnzV+/Hh9//336tGjh0aNGtXCIwRwtiF8AWjXXnjhBU2cOFHdunXTgAED1LVrV/31r39VaGioFi5cqE6dOrX0EAGcZQhfANq1p59+Wn/729/Uo0cP7dixQzabTbfffrvy8vJ04403tvTwAJyFbJb3XDsAtCPeh2rzEQjANM58AQAAGGQ8fC1cuFC//e1v1b9/f9ntdtlsNi1YsCDgdiorKzVz5kxdeeWV6tixo7p06aJ7771X+fn5te6zZcsWDR8+XJGRkQoLC9OAAQO0aNGiRswGAAAgMMGmO5w6dar27dsnp9OpqKgo7du3r0HtTJgwQXPmzFGfPn30+OOP64cfftDixYu1atUqffbZZ+rTp0+V+i6XSykpKQoJCdGoUaPkcDi0dOlSpaamqqCgQFOmTGmK6QEAANTJ+D1fn3zyiWJiYtSzZ0+99NJLysjI0Pz585WWluZ3G2vXrtVNN92kwYMHa/Xq1bLb7ZKkTz/9VMnJyRo8eLDWrVvnq19RUaG4uDgdOHBAmzZt0tVXXy3pl8eGXH/99frmm2/09ddfKyYmpknnCqD14p4vAC3F+GXHX//61+rZs2ej2pgzZ46kX34i7g1ekjRkyBClpKRo/fr1VR6Gu2bNGu3evVv33XefL3hJvzw25Nlnn1VFRYXmz5/fqDEBaFssyyJ4AWgRbfKGe5fLpbCwMN1www3VtqWkpEhSlTNfLpdLUs0rVXvLTq8PAADQXIzf89VYpaWlOnTokC6//HJ16NCh2nbvpcPTb7z3/ndNlxUjIyPldDrrvFFfkjwejzwej+/vyspK/fTTTzr//PN9ly8AAEDrZlmWSkpK1K1bNwUFtcw5qDYXvtxutyTJ4XDUuD0iIqJKPX/3OXDgQJ39zpgxQ1lZWQGPFwAAtD6FhYXq3r17i/Td5sJXS8nIyNCTTz7p+9vtdis6Olrf7tmrC8/v3IIjAwAA/iouLlaPHj0UHh7eYmNoc+HLe/bq9DNbpysuLq5Sz999ajsr5mW326vc3O8VHh7hO9sGAADahpa8ZajN3XAfFhamqKgo7d27V6dOnaq2vab7u2q6D8zr2LFjKioqYpkJAABgRJsLX5KUkJCg0tJSbdy4sdq2lStX+uqcXl+SVq1aVa2+t+z0+gAAAM2lVYevoqIi7dq1S0VFRVXKH374YUm/rJZfXl7uK//000+1cuVK3XjjjYqNjfWVDxkyRL1799aiRYv0xRdf+MpLSko0ffp0BQcHB7TIKwAAQEMZv+dr7ty5ys3NlSRt377dV+Zdi2vEiBEaMWKEJGnmzJnKyspSZmampk2b5msjKSlJ48aN09y5c3X11Vfrlltu8T1eKCIiQn/5y1+q9BkcHKy5c+cqJSVFgwcP1ujRoxUREaGlS5dq7969euGFF6qENQAAgOZiPHzl5uYqOzu7StnGjRt9lxB79erlC191efPNN3XllVfqzTff1Ouvv65zzz1Xt912m/7t3/6txiCVlJSk3NxcZWZmasmSJSovL1ffvn01ffp0paamNsncAAAA6mP82Y5nC+8vJA8dOaquTpaaAACgLfB+f7vd7hZbraBV3/MFAABwtiF8AQAAGET4AgAAMIjwBQAAYBDhCwAAwCDCFwAAgEGELwAAAIMIXwAAAAYRvgAAAAwifAEAABhE+AIAADCI8AUAAGAQ4QsAAMAgwhcAAIBBhC8AAACDCF8AAAAGEb4AAAAMInwBAAAYRPgCAAAwiPAFAABgEOELAADAIMIXAACAQYQvAAAAgwhfAAAABhG+AAAADCJ8AQAAGET4AgAAMIjwBQAAYBDhCwAAwCDCFwAAgEGELwAAAINaLHxt2bJFw4cPV2RkpMLCwjRgwAAtWrTI7/0TExNls9nqfL399ttV9unVq1etdSdMmNDUUwQAAKgmuCU6dblcSklJUUhIiEaNGiWHw6GlS5cqNTVVBQUFmjJlSr1tpKWlKTExsVr5yZMnNWPGDAUFBWnIkCHVtjscDk2cOLFaef/+/RsyFQAAgIDYLMuyTHZYUVGhuLg4HThwQJs2bdLVV18tSSopKdH111+vb775Rl9//bViYmIa1P4HH3ygu+++W7fddpv+53/+p8q2Xr16SZIKCgoaMwVJUnFxsRwOhw4dOaquzs6Nbg8AADQ/7/e32+1WREREi4zB+GXHNWvWaPfu3brvvvt8wUuSwsPD9eyzz6qiokLz589vcPtz586VJI0dO7bRYwUAAGhqxi87ulwuSdLQoUOrbfOWrVu3rkFtHzhwQKtWrVLXrl11yy231FjH4/EoOztbBw8eVGRkpAYOHKirrrqqQf0BAAAEynj4ys/Pl6QaLytGRkbK6XT66gRq/vz5qqysVFpamoKDa57a4cOHlZaWVqVs2LBhevvtt+V0Omtt2+PxyOPx+P4uLi5u0BgBAED7Zvyyo9vtlvTLje81iYiI8NUJhGVZvsuVtV1yfOihh+RyuXTkyBEVFxdr8+bNuvnmm7VixQrdfvvtquv2txkzZsjhcPhePXr0CHiMAAAAZ806X2vWrNHevXuVkJCgSy65pMY6zz33nBISEuR0OhUeHq74+HgtW7ZMgwYN0qZNm7R8+fJa28/IyJDb7fa9CgsLm2sqAADgLGY8fHnPeNV2dsv7K4RAeW+0HzduXED7BQUFKT09XZK0cePGWuvZ7XZFRERUeQEAAATKePjy3utV031dx44dU1FRUcDLTBw7dkz//d//rfPOO0+/+c1vAh6T916vsrKygPcFAAAIhPHwlZCQIElatWpVtW3eMm8dfy1cuFAej0epqanq2LFjwGPKy8uT9K91wAAAAJpLiyyyeumll+rgwYPavHmz+vXrJ6nqIqs7duxQbGysJKmoqEhFRUVyOp21/hqxX79+2rZtm7Zu3Vpl7bDTff311+rWrZvOO++8KuW5ublKTk6WZVn69ttvFR0d7dc8WGQVAIC2p10ushocHKy5c+eqsrJSgwcP1sMPP6xJkybpqquu0o4dOzRt2jRf8JKkmTNn6rLLLtPMmTNrbO///u//tG3bNl1zzTW1Bi9JWrJkibp166bbbrtNjz/+uCZNmqRhw4bpxhtv1MmTJzVz5ky/gxcAAEBDtcizHZOSkpSbm6vMzEwtWbJE5eXl6tu3r6ZPn67U1NSA2nrrrbck1X+jfVJSknbu3KmtW7dq3bp1OnHihC688EKNHDlSTzzxhAYMGNDg+QAAAPjL+GXHswWXHQEAaHva5WVHAACA9ozwBQAAYBDhCwAAwCDCFwAAgEGELwAAAIMIXwAAAAYRvgAAAAwifAEAABhE+AIAADCI8AUAAGAQ4QsAAMAgwhcAAIBBhC8AAACDCF8AAAAGEb4AAAAMInwBAAAYRPgCAAAwiPAFAABgEOELAADAIMIXAACAQYQvAAAAgwhfAAAABhG+AAAADCJ8AQAAGET4aqXKyivU64856vXHHJWVV7T0cAAAQBMhfAEAABhE+AIAADCI8AUAAGAQ4QsAAMAgwhcAAIBBhC8AAACDWix8bdmyRcOHD1dkZKTCwsI0YMAALVq0yO/9XS6XbDZbra/Nmzc3S78AAACNEdwSnbpcLqWkpCgkJESjRo2Sw+HQ0qVLlZqaqoKCAk2ZMsXvthISEpSYmFitvHv37s3aLwAAQEPYLMuyTHZYUVGhuLg4HThwQJs2bdLVV18tSSopKdH111+vb775Rl9//bViYmLqbMflcikpKUmZmZmaNm2asX69iouL5XA4dOjIUXV1dvZrn0CUlVeoz3MrJUlfP5+iTiEtkpMBADireL+/3W63IiIiWmQMxi87rlmzRrt379Z9993nC0CSFB4ermeffVYVFRWaP3/+WdMvAADA6YyfTnG5XJKkoUOHVtvmLVu3bp3f7eXn5+v1119XWVmZevbsqeTkZDmdzmbvFwAAoCGMh6/8/HxJqvHyXmRkpJxOp6+OPxYtWlTlhvmOHTsqKytLTz31VJP26/F45PF4fH8XFxf7PUYAAAAv45cd3W63JMnhcNS4PSIiwlenLl26dNErr7yinTt3qrS0VAcPHtTChQvVuXNnPf3003rzzTebtN8ZM2bI4XD4Xj169Kh3jAAAAGdqs+t89e3bV5MmTVJcXJw6deqkbt26KTU1VStWrFBISIgyMzNVWVnZZP1lZGTI7Xb7XoWFhU3WNgAAaD+Mhy/vmafazjJ5f4XQUJdffrni4+P1ww8/6Lvvvmuyfu12uyIiIqq8AAAAAmU8fHnvuarp/qpjx46pqKjI7+UeauO94b6srMxovwAAAPUxHr4SEhIkSatWraq2zVvmrdMQFRUV2rp1q2w2m6Kjo431CwAA4A/j4WvIkCHq3bu3Fi1apC+++MJXXlJSounTpys4OFhpaWm+8qKiIu3atUtFRUVV2tm0aZPOXB+2oqJCTz31lPbt26eUlBR17vyvxU8D7RcAAKA5GF9qIjg4WHPnzlVKSooGDx6s0aNHKyIiQkuXLtXevXv1wgsvKDY21ld/5syZysrKqraS/ejRo2Wz2TRw4EBddNFFOn78uNavX69vvvlG0dHRmj17dqP6BQAAaA4t8syapKQk5ebmKjMzU0uWLFF5ebn69u2r6dOnKzU11a82HnnkEa1YsUIul0tFRUUKDg7WJZdcomeeeUZ/+MMfFBkZ2Sz9AgAANIbxZzueLXi2IwAAbU+7fLYjAABAe0b4AgAAMIjwBQAAYBDhCwAAwCDCFwAAgEGELwAAAIMIXwAAAAYRvgAAAAwifAEAABhE+AIAADCI8AUAAGAQ4QsAAMAgwhcAAIBBhC8AAACDCF8AAAAGEb4AAAAMInwBAAAYRPgCAAAwiPAFAABgEOGrHSsrr1CvP+ao1x9zVFZe0dLDAQCgXSB8AQAAGET4AgAAMIjwBQAAYBDhCwAAwCDCFwAAgEGELwAAAIMIXwAAAAYRvgAAAAwifAEAABhE+AIAADCI8AUAAGBQi4WvLVu2aPjw4YqMjFRYWJgGDBigRYsW+b1/bm6u/vCHP+jaa6/V+eefr9DQUMXFxWny5Mk6fvx4jfv06tVLNputxteECROaaGYAAAC1C26JTl0ul1JSUhQSEqJRo0bJ4XBo6dKlSk1NVUFBgaZMmVJvG3fffbeKioo0aNAgPfjgg7LZbHK5XHr55Zf1wQcf6LPPPtMFF1xQbT+Hw6GJEydWK+/fv39TTA0AAKBOxsNXRUWFxo0bJ5vNpvXr1+vqq6+WJGVmZur6669XZmam7rnnHsXExNTZzhNPPKEHH3xQUVFRvjLLsvToo4/qL3/5i7KysvSf//mf1fY777zzNG3atCadEwAAgL+MX3Zcs2aNdu/erfvuu88XvCQpPDxczz77rCoqKjR//vx625k8eXKV4CVJNptNzz77rCRp3bp1TTtwAACAJmD8zJfL5ZIkDR06tNo2b1ljgtM555wjSQoOrnlqHo9H2dnZOnjwoCIjIzVw4EBdddVVDe4PAAAgEMbDV35+viTVeFkxMjJSTqfTV6ch5s2bJ6nmcCdJhw8fVlpaWpWyYcOG6e2335bT6ay1XY/HI4/H4/u7uLi4wWMEAADtl/HLjm63W9IvN77XJCIiwlcnUF988YWysrJ0wQUX6Omnn662/aGHHpLL5dKRI0dUXFyszZs36+abb9aKFSt0++23y7KsWtueMWOGHA6H79WjR48GjREAALRvZ806X3v37tWtt96qU6dO6d13363xLNZzzz2nhIQEOZ1OhYeHKz4+XsuWLdOgQYO0adMmLV++vNb2MzIy5Ha7fa/CwsLmnA4AADhLGQ9f3jNetZ3dKi4urvWsWG327dunpKQkHTlyRO+//76SkpL83jcoKEjp6emSpI0bN9Zaz263KyIiosoLAAAgUMbDl/der5ru6zp27JiKiorqXWbidAUFBUpMTNT333+vJUuW6NZbbw14TN6zZGVlZQHvCwAAEAjj4SshIUGStGrVqmrbvGXeOvXxBq+DBw9q8eLFuuOOOxo0pry8PEm/rIAPAADQnIyHryFDhqh3795atGiRvvjiC195SUmJpk+fruDg4Cq/RiwqKtKuXbtUVFRUpZ3Tg9e7776rO++8s85+v/766xofO5Sbm6t///d/l91u11133dWYqQEAANTL+FITwcHBmjt3rlJSUjR48GCNHj1aERERWrp0qfbu3asXXnhBsbGxvvozZ85UVlaWMjMzq6xMn5iYqH379um6667Tl19+qS+//LJaX6fXX7JkiV5++WUNGTJEvXr1kt1u11dffaVVq1YpKChIs2fPVnR0dHNOHQAAoGWe7ZiUlKTc3FxlZmZqyZIlKi8vV9++fTV9+nSlpqb61ca+ffskSZs3b9bmzZtrrHN6+EpKStLOnTu1detWrVu3TidOnNCFF16okSNH6oknntCAAQMaPS8AAID62Ky6FrdCrby/yjx05Ki6Ojs3eftl5RXq89xKSdLXz6eoU0jT5+SzpQ8AAPzl/f52u90ttnLBWbPOFwAAQFtA+AIAADCI8AUAAGAQ4QsAAMAgwhcAAIBBhC8AAACDCF8AAAAGEb4AAAAMInwBAAAYRPgCAAAwiPAFAABgEOELAADAIMIXAACAQYQvAAAAgwhfaPPKyivU64856vXHHJWVV7T0cAAAqBPhCwAAwCDCFwAAgEGELwAAAIMIXwAAAAYRvgAAAAwifAEAABhE+AIAADCI8AXUg3XEAABNifAFAABgEOELAADAIMIXAACAQYQvAAAAgwhfQCvATf0A0H4QvgAAAAwifAHtBGfXAKB1IHwBAAAYRPgCAAAwqMXC15YtWzR8+HBFRkYqLCxMAwYM0KJFiwJqo7KyUjNnztSVV16pjh07qkuXLrr33nuVn5/frP0CqBmXNgGgfsEt0anL5VJKSopCQkI0atQoORwOLV26VKmpqSooKNCUKVP8amfChAmaM2eO+vTpo8cff1w//PCDFi9erFWrVumzzz5Tnz59mqVfAACAhjIevioqKjRu3DjZbDatX79eV199tSQpMzNT119/vTIzM3XPPfcoJiamznbWrl2rOXPmaPDgwVq9erXsdrsk6cEHH1RycrIeeeQRrVu3rsn7PdM///lPldjPCWgff5SVn/L9d0nJP3UqpAN9tFAfZ8MczrY+4l/ZKEnKe+oGdWqG492c7QNoWSUlJS09BPPha82aNdq9e7fS09N9AUiSwsPD9eyzz2rUqFGaP3++XnzxxTrbmTNnjiTphRde8AUvSRoyZIhSUlK0YsUKffvtt4qNjW3Sfs/05bYv1dlxbkD7+MNTYfn++4t//EP2YBt9tFAfZ8Mc6KP1tO/t47eflEmS3vx1p2bpA0DNSktLW3oI5u/5crlckqShQ4dW2+YtO/2MVV3thIWF6YYbbqi2LSUlpVo7je3X4/GouLi4ygsAWitPhaW0FaVKW1FaJVACDWXi31R7+XdrsyzL6Ozuuecevf/++/r73/+ua6+9ttr2Ll26yGaz6ccff6y1jdLSUp177rm6/PLLtX379mrbc3JydOutt+qpp57Syy+/3CT9Tps2TVlZWdXKly1bprCwsFrHCgBovTgL2f6Ulpbq1ltvldvtVkRERIuMwfiZL7fbLUlyOBw1bo+IiPDVaUwbp9drin4zMjLkdrt9r8LCwjrHCABo/ezBNi0YFqYFw8IIXjCmRX7t2BbZ7fYq95YBAAA0hPEzX94zT7WdZSouLq717FQgbZxer6n6BQAAaCzjZ768Sznk5+dXu/fq2LFjKioq0sCBA+tsIywsTFFRUdq7d69OnTqlDh2q/hTcu8jq6ctGNEW/NenXr1+LXTMGAACBaQ0/mDMevhISEjRjxgytWrVKo0aNqrJt1apVvjr+tPPuu+9q48aNuvHGG6tsW7lyZbV2mqrfM4WHhys8PDzg/QAAgHmGf2dYI+O/dqyoqNCll16qgwcPavPmzerXr5+kXxY9u/766/XNN99ox44dvvW5ioqKVFRUJKfTKafT6Wtn7dq1uummmzR48GB98sknCgkJkSR9+umnSk5O1uDBg6stshpIv/XxXqZsyV9LAACAwLSG72/j93wFBwdr7ty5qqys1ODBg/Xwww9r0qRJuuqqq7Rjxw5NmzatSgCaOXOmLrvsMs2cObNKO0lJSRo3bpw2bNigq6++Wk8//bTGjBmjW265RREREfrLX/7SqH4BAACaQ4s8WDspKUm5ubkaNGiQlixZolmzZun888/XwoUL9cwzz/jdzptvvqnXX39dNptNr7/+unJycnTbbbfp888/r/Zcx6bsFwAAoKGMX3Y8W7SG05YAACAwreH7u0XOfAEAALRXhC8AAACDCF8AAAAGEb4AAAAMInwBAAAYRPgCAAAwiPAFAABgEOELAADAIMIXAACAQYQvAAAAgwhfAAAABhG+AAAADCJ8AQAAGET4AgAAMIjwBQAAYBDhCwAAwCDCFwAAgEGELwAAAIMIXwAAAAYRvgAAAAwifAEAABhE+AIAADCI8AUAAGAQ4QsAAMAgwhcAAIBBhC8AAACDCF8AAAAGEb4AAAAMInwBAAAYRPgCAAAwiPAFAABgkPHwdfjwYY0bN05RUVEKDQ1VbGysnn/+eZWXl/vdRn5+vl588UXdeOON6tatm0JCQtSjRw89+OCD2rVrV437pKWlyWaz1fiKi4trqukBAADUKdhkZ4cPH1Z8fLwKCws1YsQIxcbGKjc3V5mZmdq0aZNycnIUFFR/Hnz22We1ePFiXX755brjjjsUERGh7du36+2339b777+vlStXavDgwTXu+/vf/17nnXdelTKn09kU0wMAAKiX0fA1efJk7d+/X7NmzdIjjzwiSbIsS+np6crOzlZ2drbS09PrbWfYsGHKyMjQVVddVaX83Xff1ejRozVhwgTt2LGjxn0nTpyoXr16NXouAAAADWGzLMsy0VFJSYm6dOmiiy66SN99951sNptv26FDh9S9e3fFx8frs88+a1Q/l156qb799lsdOXKkyhmttLQ0ZWdna+/evU0SvoqLi+VwOOR2uxUREdHo9gAAQPNrDd/fxs58bdq0SR6PR8nJyVWClyRFRUXpiiuuUF5enk6cOKHQ0NAG93POOedIkoKDa55aTk6OSkpKZLfbdeWVVyoxMVEdOnRocH8AAACBMBa+8vPzJUkxMTE1bo+JidG2bdu0Z88e9enTp0F9fP7559qxY4f+3//7f9Xu6/J67LHHqvwdGxurd955R9dcc02dbXs8Hnk8Ht/fxcXFDRojAABo34z92tHtdkuSHA5Hjdu9p/689RrS/pgxYxQUFKSXX3652vaEhAR98MEHKiws1M8//6ydO3dq4sSJ2r17t4YOHarvv/++zvZnzJghh8Phe/Xo0aNB4wQAAO1bwOHL6XTWumRDTS+Xy9UMw67qxIkTuuuuu7Rr1y5Nnz5diYmJ1eqkp6frrrvuUvfu3RUaGqq4uDi99tprmjx5so4eParXXnutzj4yMjLkdrt9r8LCwmaaDQAAOJsFfNlx9OjRKikp8bt+165dJf3rjFdtZ7a8l/FqOzNWG4/HozvvvFNr1qxRRkaGpkyZEtD+Y8eO1YsvvqiNGzfWWc9ut8tutwfUNgAAwJkCDl9vvPFGgzry3uvlvffrTPn5+QoKClLv3r39bvPEiRMaMWKEVq5cqaefflovvvhiwOPy/iKyrKws4H0BAAACZeyer+uuu052u12rV6/WmatbHDp0SNu3b1d8fLzfv3Q8PXhNmjRJf/rTnxo0rry8PEli7S8AAGCEsfAVERGhkSNHas+ePZo9e7av3LIsZWRkqLKyUuPHj6+yT1lZmXbt2qX9+/dXKT9x4oTuuOMOrVy5Uk8++aReeeWVOvs+fPiwdu/eXa384MGD+t3vfifpl8upAAAAzc3YIqvSL2e44uPjdeDAAd15552KjY3Vhg0btHHjRqWkpGj58uVVHi/kcrmUlJSkhISEKjfuexdM7dq1q37729/W2FdaWprvbJbL5dJNN92kQYMGKS4uTp07d1ZBQYGWLVum0tJSjRkzRvPnz6+2/lhdWsMibQAAIDCt4fvb6OOFoqKilJeXp6lTpyonJ0fLli1TdHS0srKyNHnyZL+e6yhJBQUFkn45o5WVlVVjncTERF/4uvjiizV27Fh9/vnnev/991VSUiKHw6GBAwdq7NixGjlyZFNMDwAAoF5Gz3ydTVpDcgYAAIFpDd/fxu75AgAAAOELAADAKMIXAACAQYQvAAAAgwhfAAAABhG+AAAADCJ8AQAAGET4AgAAMIjwBQAAYBDhCwAAwCDCFwAAgEGELwAAAIMIXwAAAAYRvgAAAAwifAEAABhE+AIAADCI8AUAAGAQ4QsAAMAgwhcAAIBBhC8AAACDCF8AAAAGEb4AAAAMInwBAAAYRPgCAAAwiPAFAABgEOELAADAIMIXAACAQYQvAAAAgwhfAAAABhG+AAAADCJ8AQAAGGQ8fB0+fFjjxo1TVFSUQkNDFRsbq+eff17l5eUBtWOz2Wp9vfTSS83aNwAAQEMFm+zs8OHDio+PV2FhoUaMGKHY2Fjl5uYqMzNTmzZtUk5OjoKC/M+DPXv2VFpaWrXyQYMGNXvfAAAADWE0fE2ePFn79+/XrFmz9Mgjj0iSLMtSenq6srOzlZ2drfT0dL/b69Wrl6ZNm9YifQMAADSEzbIsy0RHJSUl6tKliy666CJ99913stlsvm2HDh1S9+7dFR8fr88++8yv9mw2mxISEuRyuYz3LUnFxcVyOBxyu92KiIjwez8AANByWsP3t7EzX5s2bZLH41FycnKV8CNJUVFRuuKKK5SXl6cTJ04oNDTUrzaPHz+uuXPn6scff1SXLl2UmJiomJgYI30DAAA0hLHwlZ+fL0k1hiNv+bZt27Rnzx716dPHrza3bdum8ePH+/622WxKTU3Vm2++qU6dOjVp3x6PRx6Px/d3cXGxX2MEAAA4nbE7zN1utyTJ4XDUuN176s9brz6TJk1SXl6efvrpJx07dkxr1qxRfHy8Fi5cqLFjxzZ53zNmzJDD4fC9evTo4dc4AQAAThdw+HI6nXUu83Dmy597shrilVde0YABAxQZGanzzjtPSUlJ+vTTT3XJJZfo3Xff1Y4dO5q0v4yMDLndbt+rsLCwSdsHAADtQ8CXHUePHq2SkhK/63ft2lXSv8461XZ2yXsZr7azU/7o1KmTRo8erenTp2vjxo3q27dvk/Vtt9tlt9sbPDYAAACpAeHrjTfeaFBH3vutvPdfnSk/P19BQUHq3bt3g9r3cjqdkqSysjLjfQMAANTH2D1f1113nex2u1avXq0zV7c4dOiQtm/frvj4+Eb/2jAvL0/SL2uAme4bAACgPsbCV0REhEaOHKk9e/Zo9uzZvnLLspSRkaHKysoqv1yUfjl7tWvXLu3fv79K+T/+8Y8qZ7a83nvvPb3zzjtyOp369a9/3ai+AQAAmoOxRValX84yxcfH68CBA7rzzjsVGxurDRs2aOPGjUpJSdHy5curPOLH5XIpKSmp2mKqaWlp+vDDDzVkyBBFR0fLsixt3bpVGzZsUGhoqD744AMNHz68UX3XpzUs0gYAAALTGr6/jT5eKCoqSnl5eZo6dapycnK0bNkyRUdHKysrS5MnT/Y7/Nxxxx06fvy4tm7dqhUrVqiiokIXXXSRxo4dq0mTJikuLq7Z+gYAAGgMo2e+ziatITkDAIDAtIbvb073AAAAGET4AgAAMIjwBQAAYBDhCwAAwCDCFwAAgEGELwAAAIMIXwAAAAYRvgAAAAwifAEAABhE+AIAADCI8AUAAGAQ4QsAAMAgwhcAAIBBhC8AAACDCF8AAAAGEb4AAAAMInwBAAAYRPgCAAAwiPAFAABgEOELAADAIMIXAACAQYQvAAAAgwhfAAAABhG+AAAADCJ8AQAAGET4AgAAMIjwBQAAYBDhCwAAwCDCFwAAgEGELwAAAIMIXwAAAAYZD1+HDx/WuHHjFBUVpdDQUMXGxur5559XeXm5321MmzZNNputztfYsWOr7JOWllZr3bi4uKaeJgAAQI2CTXZ2+PBhxcfHq7CwUCNGjFBsbKxyc3OVmZmpTZs2KScnR0FB9efBxMTEWrfNnTtXBw8eVEpKSo3bf//73+u8886rUuZ0OgOZBgAAQIPZLMuyTHU2ZswY/fWvf9WsWbP0yCOPSJIsy1J6erqys7M1b948paenN7j9H374Qd27d5fD4dD333+vkJAQ37a0tDRlZ2dr79696tWrV2OnouLiYjkcDrndbkVERDS6PQAA0Pxaw/e3scuOJSUlWrx4sXr37q0JEyb4ym02m2bMmKGgoCDNmTOnUX0sWLBAFRUVeuCBB6oELwAAgNbC2GXHTZs2yePxKDk5WTabrcq2qKgoXXHFFcrLy9OJEycUGhraoD7mzZsnSRo3blytdXJyclRSUiK73a4rr7xSiYmJ6tChQ4P6AwAACJSx8JWfny9JiomJqXF7TEyMtm3bpj179qhPnz4Bt79hwwZ9++23uu6669S3b99a6z322GNV/o6NjdU777yja665ps72PR6PPB6P7+/i4uKAxwgAAGDssqPb7ZYkORyOGrd7r7t66wXqrbfeklT7Wa+EhAR98MEHKiws1M8//6ydO3dq4sSJ2r17t4YOHarvv/++zvZnzJghh8Phe/Xo0aNB4wQAAO1bwOHL6XTWu8zD6S+Xy9UMw66quLhY7733ns4991yNHDmyxjrp6em666671L17d4WGhiouLk6vvfaaJk+erKNHj+q1116rs4+MjAy53W7fq7CwsDmmAgAAznIBX3YcPXq0SkpK/K7ftWtXSf8641XbmS3vZbzazozV5Z133lFZWZnGjh2rc889N6B9x44dqxdffFEbN26ss57dbpfdbg94bAAAAKcLOHy98cYbDerIe6+X996vM+Xn5ysoKEi9e/cOuO36LjnWxbvGV1lZWcD7AgAABMrYPV/XXXed7Ha7Vq9erTOXFjt06JC2b9+u+Pj4gH/puH37dm3ZskV9+/bVddddF/C48vLyJKlJ1v4CAACoj7HwFRERoZEjR2rPnj2aPXu2r9yyLGVkZKiyslLjx4+vsk9ZWZl27dql/fv319qu96zXmY8TOt3hw4e1e/fuauUHDx7U7373O0m/XE4FAABobkZXuD906JDi4+N14MAB3XnnnYqNjdWGDRu0ceNGpaSkaPny5VUeL+RyuZSUlKSEhIQab9wvLy9Xt27dVFJSooMHD9b6mCCXy6WbbrpJgwYNUlxcnDp37qyCggItW7ZMpaWlGjNmjObPn19t/bG6tIYVcgEAQGBaw/e30Wc7RkVFKS8vT1OnTlVOTo6WLVum6OhoZWVlafLkyX491/F0H374oY4ePap77723zuczXnzxxRo7dqw+//xzvf/++yopKZHD4dDAgQM1duzYWn8hCQAA0NSMnvk6m7SG5AwAAALTGr6/jd3zBQAAAMIXAACAUYQvAAAAgwhfAAAABhG+AAAADCJ8AQAAGET4AgAAMIjwBQAAYBDhCwAAwCDCFwAAgEGELwAAAIMIXwAAAAYRvgAAAAwifAEAABhE+AIAADCI8AUAAGAQ4QsAAMAgwhcAAIBBhC8AAACDCF8AAAAGEb4AAAAMInwBAAAYRPgCAAAwiPAFAABgEOELAADAIMIXAACAQYQvAAAAgwhfAAAABhG+AAAADCJ8AQAAGET4AgAAMMho+Fq/fr0mTZqkpKQkORwO2Ww2paWlNbi9lStXKjExUREREQoPD1diYqJWrlxZa/3Dhw9r3LhxioqKUmhoqGJjY/X888+rvLy8wWMAAAAIRLDJzubNm6fs7Gx16tRJ0dHRKi4ubnBbf/vb33T//ffL6XRqzJgxstlsWrJkiYYNG6aFCxcqNTW1Sv3Dhw8rPj5ehYWFGjFihGJjY5Wbm6vMzExt2rRJOTk5CgriRCAAAGheNsuyLFOd/f3vf1fHjh0VFxenLVu26Prrr9eYMWO0YMGCgNo5duyYevfureDgYG3dulU9evSQJB06dEjXXHONTpw4oT179igyMtK3z5gxY/TXv/5Vs2bN0iOPPCJJsixL6enpys7O1rx585Senu73GIqLi+VwOOR2uxURERHQ+AEAQMtoDd/fRk/19O/fX3379lWHDh0a1c57772n48eP6/HHH/cFL0mKiorSxIkTdfz4cb333nu+8pKSEi1evFi9e/fWhAkTfOU2m00zZsxQUFCQ5syZ06gxAQAA+KNNXmdzuVySpKFDh1bblpKSIklat26dr2zTpk3yeDxKTk6WzWarUj8qKkpXXHGF8vLydOLEieYbNAAAgAzf89VU8vPzJUkxMTHVtnnLvHXqq+8t37Ztm/bs2aM+ffrUWMfj8cjj8fj+drvdktSo+9YAAIBZ3u9tg3ddVdMmw5c3+DgcjmrbwsLC1KFDB1+d+upL8l3zPX2fM82YMUNZWVnVyk+/7AkAANqGo0eP1poLmlvA4cvpdOro0aN+11+7dq0SExMD7abVycjI0JNPPun7+/jx4+rZs6f279/fYgevJRQXF6tHjx4qLCxsVz80YN7Muz1g3sy7PXC73YqOjlbnzp1bbAwBh6/Ro0erpKTE7/pdu3YNtIt6ecOO2+3W+eefX2VbaWmpTp06VSUQnV6/Jt5TkHWFKLvdLrvdXuNY2tM/Wq+IiAjm3Y4w7/aFebcv7XXeLbm8VMDh64033miOcQQkJiZGf//735Wfn18tfNV0f1dN94GduU9QUJB69+7dTCMGAAD4RZv8tWNCQoIkadWqVdW2eVe499aRpOuuu052u12rV6+udoPdoUOHtH37dsXHxys0NLQZRw0AANDKw1dZWZl27dql/fv3Vym/99575XA49MYbb6iwsNBXfujQIf35z3/Weeedp3vuucdXHhERoZEjR2rPnj2aPXu2r9yyLGVkZKiyslLjx48PaGx2u12ZmZk1Xoo8mzFv5t0eMG/m3R4w75abt9EV7nNzczV37lxJ0pEjR7R8+XJdfPHFGjRokCQpLi5Of/zjH331XS6XkpKSlJCQ4Fvby2vhwoV64IEH5HQ6NWrUKAUFBWnx4sX64Ycf9Pbbb+v++++vUv/QoUOKj4/XgQMHdOeddyo2NlYbNmzQxo0blZKSouXLl/N4IQAA0OyMhq8FCxbU+QifM0NWXeFLklasWKEZM2Zo69atkqRrrrlGU6ZM8S20eqZDhw5p6tSpysnJ0bFjxxQdHa0HHnhAkydPbnfJHwAAtAyj4QsAAKC94zobAACAQYQvAAAAgwhfAAAABhG+TrNlyxYNHz5ckZGRCgsL04ABA7Ro0aKA2qisrNTMmTN15ZVXqmPHjurSpYvuvffeWhd4bUkHDx7Un//8Zw0dOlTR0dEKCQlR165d9Zvf/EZ5eXl+t+NyuWSz2Wp9bd68uRln0TC9evWqdbwTJkzwu522dLwXLFhQ53Gy2WwaMmRIve205uO9cOFC/fa3v1X//v1lt9tls9m0YMGCWusXFxfrySefVM+ePWW329WzZ089+eSTvqdeBKIpPj8ayt95nzx5Uh988IHS0tJ02WWXKSwsTOHh4YqPj9esWbN06tSpgPptqvdRQwVyvKdNm1brWBuyxmNbON6S6n3P22y2Kks21aUlj3dDvq9a8/u7TT5Yuzm4XC6lpKQoJCREo0aNksPh0NKlS5WamqqCggJNmTLFr3YmTJigOXPmqE+fPnr88cf1ww8/aPHixVq1apU+++wz9enTp5ln4r833nhDf/rTn3TxxRcrOTlZF1xwgfLz8/Xhhx/qww8/1DvvvKN7773X7/YSEhJqfI5n9+7dm3DUTcfhcGjixInVyvv37+93G23pePfr10+ZmZk1bnv//fe1Y8eOWn8pXJPWeLynTp2qffv2yel0KioqSvv27au1bmlpqRISEvTFF18oOTlZo0eP1rZt2/Taa69p7dq1ys3NVVhYmF/9NtXnR0P5O+/du3fr7rvvVnh4uG666Sbdfvvtcrvd+t///V89+uijWrFihT766CPZbDa/+26K91FDBXK8vcaMGaNevXpVKQsODuyrsK0cb0m1vue/++47/e1vf9Nll12mHj16+N13Sx3vQL+vWv3724J18uRJ6+KLL7bsdru1detWX3lxcbHVt29fKzg42Pr222/rbWfNmjWWJGvw4MHWiRMnfOWffPKJZbPZrBtvvLFZxt9QH3zwgbV+/fpq5evXr7fOOeccq3PnzlXmUZu1a9dakqzMzMxmGGXz6Nmzp9WzZ89GtdHWjndtPB6Pdf7551vBwcHW4cOH663fmo/36tWrrYKCAsuyLGvGjBmWJGv+/Pk11n3uuecsSdbTTz9dY/lzzz3nV59N9fnRGP7O+8CBA9asWbOs0tLSKuX//Oc/rf79+1uSrCVLlvjdb1O8jxojkOOdmZlpSbLWrl3bqD7b0vGuy2OPPWZJsl599VW/92nJ4x3o91Vrf38TvizLWrlypSXJSk9Pr7bt3XfftSRZGRkZ9bYzevRoS5K1bt26atuGDRtmSbK++eabJhlzcxs6dKglydqyZUu9dVvzl3FtmuJD5Gw53t5/4yNGjPCrfls53nV9KVVWVlrdunWzzj33XOuf//xnlW0///yzFRkZaV100UVWZWVlvf001edHU2nol/GiRYssSdajjz7q9z4tHb5OZyp8nQ3H2/tvPCQkxPrxxx/93q81He/Tnfl91Rbe31x2lHwLuA4dOrTaNm/ZunXr/GonLCxMN9xwQ7VtKSkpWrFihdatW6fY2NjGDdiAc845R1Jgp+Pz8/P1+uuvq6ysTD179lRycrKcTmdzDbHRPB6PsrOzdfDgQUVGRmrgwIG66qqr/N7/bDneb731liRp3LhxAe3X1o736fLz8/X9998rJSWl2qWH0NBQ3Xjjjfroo4/03XffKSYmps62murzo6U15D0vNf59ZNqGDRv0+eefq0OHDoqLi9Ovf/3rgBbZPhuO99KlS3Xs2DHdfffd6tKlS0D7tsbjfea/3bbw/iZ8Sb6bo2s6CJGRkXI6nfXeQF1aWqpDhw7p8ssvV4cOHapt97bdGm/EPtP+/fv1ySefqGvXrrriiiv83m/RokVVbkDs2LGjsrKy9NRTTzXHMBvt8OHDSktLq1I2bNgwvf322/WGiLPleO/bt0+ffvqpLrroIg0bNiygfdva8T5dXe/508vz8/Pr/XBuis+P1mDevHmSav6SqUtj3kct4bnnnqvyd1RUlLKzs5WcnOzX/mfD8W7o/3BJre941/R91Rbe3/zaUZLb7Zb0y42ENYmIiPDVaUwbp9drrU6ePKkHHnhAHo9HL7/8co3B4kxdunTRK6+8op07d6q0tFQHDx7UwoUL1blzZz399NN68803DYw8MA899JBcLpeOHDmi4uJibd68WTfffLNWrFih22+/XVY9D344W473/PnzVVlZqfT0dL+OtdQ2j/eZmvL4NcXnR0v7r//6L3388ce66aabNHz4cL/3a+z7yKR+/fopOztbBQUF+vnnn5Wfn6/p06fr+PHjuv3227Vt2za/2mnrx3vv3r1au3atoqOj/Q6cXq3teNf2fdUW3t+c+YJPZWWlHnroIa1fv17jx4/XAw884Nd+ffv2Vd++fX1/d+rUSampqbrqqqt07bXXKjMzU+PHj29VDy4/8/9+4+PjtWzZMiUkJCg3N1fLly/XLbfc0kKjM6OyslLz58+XzWbTQw895Pd+bfF4o3Y5OTl67LHH1LNnTy1cuDCgfdvS+2jEiBFV/r7kkks0depUXXjhhXr44Yf1wgsv6L333muZwRk0b948WZal9PT0gN+jrel4N/T7qrXg01H/SrS1pdfi4uJaU28gbZxer7WxLEvjx4/XwoULdf/992v27NmNbvPyyy9XfHy8fvjhB3333XdNMMrmFRQU5Hvw+8aNG+us29aPtyStXr1a+/fv10033aRf/epXjW6vLR3vpjx+TfH50VJWrlyp3/zmN7rwwgu1Zs0aRUVFNbrNQN5HrcGYMWMUHBzs91jb8vGurKzUggULFBQUFND/cNWlJY53fd9XbeH9TfhS3ffnHDt2TEVFRfVeFw4LC1NUVJT27t1b40KF9V2DbkmVlZUaO3as5s2bp9GjR/venE3Bew9AWVlZk7TX3Pwdb1s+3l6Nue+jNm3leNd3T14gx68pPj9awooVKzRixAg5nU6tXbtWvXv3brK228q/A0kKCQlReHi432Ntq8db+uWYHzhwQMnJyYqOjm6ydk0eb3++r9rC+5vwpV8Wi5SkVatWVdvmLfPWqa+d0tLSGtP/ypUr/W7HpMrKSo0bN07z58/XyJEj9fbbb/t97099KioqtHXrVtlstiZ9ozcn70rJZy7CWJO2eLy9jh49qo8++kidO3fWnXfe2SRttqXjHRMTo27dumnjxo0qLS2tsu3EiRNav369unXrpksuuaTetprq88Mkb/CKjIzU2rVr/ZpnIAJ5H7W0/Px8HTt2zO+xtsXj7dUc/8MlmTve/n5ftYn3d8CLU5yFTp48afXu3duy2+3WP/7xD1/56Yuonb5e05EjR6ydO3daR44cqdLO6YtuejweX3lrXXTz1KlTVlpamiXJuueee6yTJ0/WWb+2eX/22WfV1ks5efKkNXHiREuSNWzYsCYfe2Ps2LHDOnbsWLXyDRs2WKGhoZbdbrf27dvnKz9bjvfpXnvtNUuS9bvf/a7WOm39eDf1Iqvl5eXWzp07re+++65KeaCfH82tvnl//PHHlt1ut7p27Wrt2rWr3vZqm3eg76PmVte8i4uLrW3btlUr/+mnn6zBgwdbkqyXXnqpyraz5Xh7/fjjj9Y555xjOZ3OKp9XZ2qtxzvQ76vW/v62WVYr+jlKC1q7dq1SUlJkt9s1evRoRUREaOnSpdq7d69eeOEFPfPMM76606ZNU1ZWljIzMzVt2rQq7YwfP15z585Vnz59dMstt/geNxMaGtrqHjfjnce5556r3//+9zWu7zNixAj169evSv0z5+193tfAgQN10UUX6fjx41q/fr2++eYbRUdHa/369erZs6ehWdVv2rRpevnllzVkyBD16tVLdrtdX331lVatWqWgoCDNnj27yv8Zni3H+3RXXHGFvvrqK3355Ze1LifSFo/33LlzlZubK0navn27tm7dqhtuuMH3f7gjRozw3XhdWlqqQYMG+R4/cu2112rbtm36+OOP1a9fv2qPHykoKNCvfvUr9ezZUwUFBVX6DeTzoyXnvWvXLvXr108ej0ejRo3SpZdeWq2tXr16VVlKoLZ5B/o+asl5e+fQv39/XXHFFbrgggt08OBBffzxxzp69KiSk5O1bNkyhYSE1Dtvqe0c79O9+uqrmjRpkp588km9+uqrtbbdWo93oN9Xrf79HXBcO4vl5eVZw4YNsxwOh9WxY0erf//+1sKFC6vV866UXNMK36dOnbJef/11q2/fvpbdbrfOP/986+67726VK52PGTPGklTn6/T/m6pt3i+99JKVmJhodevWzQoJCbE6depkXXnlldYzzzxj/fTTT2Yn5QeXy2Xde++91iWXXGKFh4db55xzjtW9e3dr1KhRVl5eXrX6Z8vx9srLy7MkWQMGDKizXls83vX9mz5zLsePH7eeeOIJq0ePHtY555xj9ejRw3riiSes48ePV2t77969lqRaV/j29/OjOfg7b+/TCep6JSQkVGm7tnkH+j5qyXm73W7r0Ucfta699lrL6XRawcHBlsPhsAYNGmTNnj3bqqioqNb22XC8T3fZZZdZkqyvv/66zrZb6/EO9PvKslr3+5szXwAAAAZxwz0AAIBBhC8AAACDCF8AAAAGEb4AAAAMInwBAAAYRPgCAAAwiPAFAABgEOELAADAIMIXAACAQYQvAAAAgwhfAAAABhG+AAAADPr/rAZgqms9bmgAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = az.plot_autocorr(trace, max_lag=20, combined=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们使用 arviz 的 `summary`来获得对于 MCMC 链的 R-hat和 有效样本量 ESS 指标。  \n",
    "\n",
    "- 可以看到 r-hat 接近1，表明链间和各链内的变异的一致性。  \n",
    "- 有效样本量 ESS (ess_bulk) 为 4744，有效样本量比率 4744/5000 = 0.95，远大于 0.1。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>pi</th>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>4744.0</td>\n",
       "      <td>4366.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mcse_mean  mcse_sd  ess_bulk  ess_tail  r_hat\n",
       "pi      0.001    0.001    4744.0    4366.0    1.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(trace, kind = \"diagnostics\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "虽然示例的 trace 不存在强烈的自相关，但我们演示如何通过 thin 参数来使得采样更薄，从而减少链的自相关。  \n",
    "\n",
    "- 我们设置 thin 为10，即每隔10保留一个参数，这导致样本数量只有之前的 1/10，即500  \n",
    "- 可以看到，自相关几乎不存在了。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n",
       "<defs>\n",
       "<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n",
       "<path d=\"M16 0c-8.837 0-16 2.239-16 5v4c0 2.761 7.163 5 16 5s16-2.239 16-5v-4c0-2.761-7.163-5-16-5z\"></path>\n",
       "<path d=\"M16 17c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
       "<path d=\"M16 26c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
       "</symbol>\n",
       "<symbol id=\"icon-file-text2\" viewBox=\"0 0 32 32\">\n",
       "<path d=\"M28.681 7.159c-0.694-0.947-1.662-2.053-2.724-3.116s-2.169-2.030-3.116-2.724c-1.612-1.182-2.393-1.319-2.841-1.319h-15.5c-1.378 0-2.5 1.121-2.5 2.5v27c0 1.378 1.122 2.5 2.5 2.5h23c1.378 0 2.5-1.122 2.5-2.5v-19.5c0-0.448-0.137-1.23-1.319-2.841zM24.543 5.457c0.959 0.959 1.712 1.825 2.268 2.543h-4.811v-4.811c0.718 0.556 1.584 1.309 2.543 2.268zM28 29.5c0 0.271-0.229 0.5-0.5 0.5h-23c-0.271 0-0.5-0.229-0.5-0.5v-27c0-0.271 0.229-0.5 0.5-0.5 0 0 15.499-0 15.5 0v7c0 0.552 0.448 1 1 1h7v19.5z\"></path>\n",
       "<path d=\"M23 26h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
       "<path d=\"M23 22h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
       "<path d=\"M23 18h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
       "</symbol>\n",
       "</defs>\n",
       "</svg>\n",
       "<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n",
       " *\n",
       " */\n",
       "\n",
       ":root {\n",
       "  --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n",
       "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
       "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
       "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
       "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
       "  --xr-background-color: var(--jp-layout-color0, white);\n",
       "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
       "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
       "}\n",
       "\n",
       "html[theme=dark],\n",
       "body[data-theme=dark],\n",
       "body.vscode-dark {\n",
       "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
       "  --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
       "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
       "  --xr-border-color: #1F1F1F;\n",
       "  --xr-disabled-color: #515151;\n",
       "  --xr-background-color: #111111;\n",
       "  --xr-background-color-row-even: #111111;\n",
       "  --xr-background-color-row-odd: #313131;\n",
       "}\n",
       "\n",
       ".xr-wrap {\n",
       "  display: block !important;\n",
       "  min-width: 300px;\n",
       "  max-width: 700px;\n",
       "}\n",
       "\n",
       ".xr-text-repr-fallback {\n",
       "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-header {\n",
       "  padding-top: 6px;\n",
       "  padding-bottom: 6px;\n",
       "  margin-bottom: 4px;\n",
       "  border-bottom: solid 1px var(--xr-border-color);\n",
       "}\n",
       "\n",
       ".xr-header > div,\n",
       ".xr-header > ul {\n",
       "  display: inline;\n",
       "  margin-top: 0;\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-obj-type,\n",
       ".xr-array-name {\n",
       "  margin-left: 2px;\n",
       "  margin-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-obj-type {\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-sections {\n",
       "  padding-left: 0 !important;\n",
       "  display: grid;\n",
       "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
       "}\n",
       "\n",
       ".xr-section-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-section-item input {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-section-item input + label {\n",
       "  color: var(--xr-disabled-color);\n",
       "}\n",
       "\n",
       ".xr-section-item input:enabled + label {\n",
       "  cursor: pointer;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-section-item input:enabled + label:hover {\n",
       "  color: var(--xr-font-color0);\n",
       "}\n",
       "\n",
       ".xr-section-summary {\n",
       "  grid-column: 1;\n",
       "  color: var(--xr-font-color2);\n",
       "  font-weight: 500;\n",
       "}\n",
       "\n",
       ".xr-section-summary > span {\n",
       "  display: inline-block;\n",
       "  padding-left: 0.5em;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:disabled + label {\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-section-summary-in + label:before {\n",
       "  display: inline-block;\n",
       "  content: '►';\n",
       "  font-size: 11px;\n",
       "  width: 15px;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:disabled + label:before {\n",
       "  color: var(--xr-disabled-color);\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label:before {\n",
       "  content: '▼';\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label > span {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-section-summary,\n",
       ".xr-section-inline-details {\n",
       "  padding-top: 4px;\n",
       "  padding-bottom: 4px;\n",
       "}\n",
       "\n",
       ".xr-section-inline-details {\n",
       "  grid-column: 2 / -1;\n",
       "}\n",
       "\n",
       ".xr-section-details {\n",
       "  display: none;\n",
       "  grid-column: 1 / -1;\n",
       "  margin-bottom: 5px;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked ~ .xr-section-details {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-array-wrap {\n",
       "  grid-column: 1 / -1;\n",
       "  display: grid;\n",
       "  grid-template-columns: 20px auto;\n",
       "}\n",
       "\n",
       ".xr-array-wrap > label {\n",
       "  grid-column: 1;\n",
       "  vertical-align: top;\n",
       "}\n",
       "\n",
       ".xr-preview {\n",
       "  color: var(--xr-font-color3);\n",
       "}\n",
       "\n",
       ".xr-array-preview,\n",
       ".xr-array-data {\n",
       "  padding: 0 5px !important;\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-array-data,\n",
       ".xr-array-in:checked ~ .xr-array-preview {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
       ".xr-array-preview {\n",
       "  display: inline-block;\n",
       "}\n",
       "\n",
       ".xr-dim-list {\n",
       "  display: inline-block !important;\n",
       "  list-style: none;\n",
       "  padding: 0 !important;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list:before {\n",
       "  content: '(';\n",
       "}\n",
       "\n",
       ".xr-dim-list:after {\n",
       "  content: ')';\n",
       "}\n",
       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
       "  content: ',';\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-has-index {\n",
       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
       ".xr-var-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-var-item > div,\n",
       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
       ".xr-var-list > li:nth-child(odd) > label,\n",
       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-odd);\n",
       "}\n",
       "\n",
       ".xr-var-name {\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-var-dims {\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-var-dtype {\n",
       "  grid-column: 3;\n",
       "  text-align: right;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-preview {\n",
       "  grid-column: 4;\n",
       "}\n",
       "\n",
       ".xr-index-preview {\n",
       "  grid-column: 2 / 5;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-name,\n",
       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
       ".xr-preview,\n",
       ".xr-attrs dt {\n",
       "  white-space: nowrap;\n",
       "  overflow: hidden;\n",
       "  text-overflow: ellipsis;\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
       "}\n",
       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data,\n",
       ".xr-index-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data,\n",
       ".xr-index-data-in:checked ~ .xr-index-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-index-name div,\n",
       ".xr-index-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data,\n",
       ".xr-index-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2,\n",
       ".xr-no-icon {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:  (chain: 4, draw: 500)\n",
       "Coordinates:\n",
       "  * chain    (chain) int32 0 1 2 3\n",
       "  * draw     (draw) int32 0 10 20 30 40 50 60 ... 4940 4950 4960 4970 4980 4990\n",
       "Data variables:\n",
       "    pi       (chain, draw) float64 0.6946 0.9428 0.8367 ... 0.8636 0.8551 0.8676\n",
       "Attributes:\n",
       "    created_at:                 2024-10-30T01:47:15.618820\n",
       "    arviz_version:              0.17.1\n",
       "    inference_library:          pymc\n",
       "    inference_library_version:  5.16.2\n",
       "    sampling_time:              31.287054538726807\n",
       "    tuning_steps:               0</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-8bf044b0-a3ad-4d63-9525-d57f1b52ebe5' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-8bf044b0-a3ad-4d63-9525-d57f1b52ebe5' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 4</li><li><span class='xr-has-index'>draw</span>: 500</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-c610555f-1f78-4351-8a64-178862cecdce' class='xr-section-summary-in' type='checkbox'  checked><label for='section-c610555f-1f78-4351-8a64-178862cecdce' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int32</div><div class='xr-var-preview xr-preview'>0 1 2 3</div><input id='attrs-8c48641c-4d61-43a1-92d6-e49d72549df2' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-8c48641c-4d61-43a1-92d6-e49d72549df2' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-8543edd5-2b50-4ebb-8282-42f7783a4627' class='xr-var-data-in' type='checkbox'><label for='data-8543edd5-2b50-4ebb-8282-42f7783a4627' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1, 2, 3])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int32</div><div class='xr-var-preview xr-preview'>0 10 20 30 ... 4960 4970 4980 4990</div><input id='attrs-b12a8e16-4d04-4b4a-bff0-4ee74bdb258c' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b12a8e16-4d04-4b4a-bff0-4ee74bdb258c' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-d5794c4d-5b1c-4955-9523-8647dbcfa954' class='xr-var-data-in' type='checkbox'><label for='data-d5794c4d-5b1c-4955-9523-8647dbcfa954' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([   0,   10,   20, ..., 4970, 4980, 4990])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-0ca3c189-ea86-4e3d-94e7-aee3c39d3981' class='xr-section-summary-in' type='checkbox'  checked><label for='section-0ca3c189-ea86-4e3d-94e7-aee3c39d3981' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>pi</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.6946 0.9428 ... 0.8551 0.8676</div><input id='attrs-9440f718-f386-4535-b1a2-1679341b91c6' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-9440f718-f386-4535-b1a2-1679341b91c6' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-6df13f21-b621-4af9-89c8-d054868df2a1' class='xr-var-data-in' type='checkbox'><label for='data-6df13f21-b621-4af9-89c8-d054868df2a1' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.69459658, 0.94278139, 0.83667045, ..., 0.72543572, 0.77218586,\n",
       "        0.79339494],\n",
       "       [0.83451846, 0.93718211, 0.79875923, ..., 0.73197361, 0.74135104,\n",
       "        0.67311654],\n",
       "       [0.91612668, 0.87065615, 0.90718409, ..., 0.53466908, 0.88057703,\n",
       "        0.90598199],\n",
       "       [0.81972277, 0.77083496, 0.76215542, ..., 0.86357788, 0.85514079,\n",
       "        0.86764909]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-6c3006be-c245-452d-b1bc-8547367faf36' class='xr-section-summary-in' type='checkbox'  ><label for='section-6c3006be-c245-452d-b1bc-8547367faf36' class='xr-section-summary' >Indexes: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>chain</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-41184bdb-a209-4c92-9703-2657eff8b785' class='xr-index-data-in' type='checkbox'/><label for='index-41184bdb-a209-4c92-9703-2657eff8b785' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([0, 1, 2, 3], dtype=&#x27;int32&#x27;, name=&#x27;chain&#x27;))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>draw</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-9463ef0f-1fae-4267-ad11-3cf5a8aab46b' class='xr-index-data-in' type='checkbox'/><label for='index-9463ef0f-1fae-4267-ad11-3cf5a8aab46b' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([   0,   10,   20,   30,   40,   50,   60,   70,   80,   90,\n",
       "       ...\n",
       "       4900, 4910, 4920, 4930, 4940, 4950, 4960, 4970, 4980, 4990],\n",
       "      dtype=&#x27;int32&#x27;, name=&#x27;draw&#x27;, length=500))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-2fa89525-b310-4f2a-84b1-eb065e88c9e7' class='xr-section-summary-in' type='checkbox'  checked><label for='section-2fa89525-b310-4f2a-84b1-eb065e88c9e7' class='xr-section-summary' >Attributes: <span>(6)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2024-10-30T01:47:15.618820</dd><dt><span>arviz_version :</span></dt><dd>0.17.1</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.16.2</dd><dt><span>sampling_time :</span></dt><dd>31.287054538726807</dd><dt><span>tuning_steps :</span></dt><dd>0</dd></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.Dataset>\n",
       "Dimensions:  (chain: 4, draw: 500)\n",
       "Coordinates:\n",
       "  * chain    (chain) int32 0 1 2 3\n",
       "  * draw     (draw) int32 0 10 20 30 40 50 60 ... 4940 4950 4960 4970 4980 4990\n",
       "Data variables:\n",
       "    pi       (chain, draw) float64 0.6946 0.9428 0.8367 ... 0.8636 0.8551 0.8676\n",
       "Attributes:\n",
       "    created_at:                 2024-10-30T01:47:15.618820\n",
       "    arviz_version:              0.17.1\n",
       "    inference_library:          pymc\n",
       "    inference_library_version:  5.16.2\n",
       "    sampling_time:              31.287054538726807\n",
       "    tuning_steps:               0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "thinned_trace = trace.sel(draw=slice(None, None, 10))\n",
    "\n",
    "# 注意，thinned_trace 只有 500个采样\n",
    "thinned_trace.posterior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 700x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(7, 3))\n",
    "\n",
    "az.plot_autocorr(trace, max_lag=10, combined=True, ax=axes[0])\n",
    "axes[0].set_title('Full Trace')\n",
    "az.plot_autocorr(thinned_trace, max_lag=10, combined=True, ax=axes[1])\n",
    "axes[1].set_title('Thinned trace')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Posterior estimation  \n",
    "\n",
    "当我们确定 MCMC 采样的结果的可信后，我们就可以将其**当作后验分布**进行统计推断。\n",
    "\n",
    "在此之前，我们需要回顾后验分布的含义和意义。\n",
    "\n",
    "**在贝叶斯的框架下，我们可以把后验分布看作是对成功次数$\\pi$的一种估计，即当前数据更可能在哪一种$\\pi$下出现。**  \n",
    "\n",
    "> 🤔当你看到这个后验分布时，你觉得它描述了关于$\\pi$怎样的一种信息呢？  \n",
    "> * a. 参与者正确判断的概率大概在80%  \n",
    "> * b. 参与者正确判断的概率比例最有可能是80%，但这个比例也可能是60%到99%中的某一个。  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# 导入数字和向量处理包：numpy\n",
    "import numpy as np\n",
    "# 导入基本绘图工具：matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "# 导入高级绘图工具 seaborn 为 sns\n",
    "import seaborn as sns\n",
    "# 导入概率分布计算和可视化包：preliz\n",
    "import preliz as pz\n",
    "\n",
    "def bayesian_analysis_plot(\n",
    "    alpha, beta, y, n, \n",
    "    ax=None, \n",
    "    plot_prior=True, \n",
    "    plot_likelihood=True, \n",
    "    plot_posterior=True, \n",
    "    xlabel=r\"$\\pi$\", \n",
    "    show_legend=True,\n",
    "    legend_loc=\"upper left\"):\n",
    "    \"\"\"\n",
    "    该函数绘制先验分布、似然分布和后验分布的 PDF 图示在指定的子图上。\n",
    "    \n",
    "    参数:\n",
    "    - alpha: Beta 分布的 alpha 参数（先验）\n",
    "    - beta: Beta 分布的 beta 参数（先验）\n",
    "    - y: 观测数据中的支持次数\n",
    "    - n: 总样本数\n",
    "    - ax: 子图对象，在指定子图上绘制图形\n",
    "    \"\"\"\n",
    "\n",
    "    if ax is None:\n",
    "        ax = plt.gca()\n",
    "\n",
    "    if plot_prior:\n",
    "        # 先验分布\n",
    "        prior = pz.Beta(alpha, beta)\n",
    "        prior.plot_pdf(color=\"black\", ax=ax, legend=\"None\")\n",
    "        x_prior = np.linspace(prior.ppf(0.0001), prior.ppf(0.9999), 100)\n",
    "        ax.fill_between(x_prior, prior.pdf(x_prior), color=\"#f0e442\", alpha=0.5, label=\"prior\")\n",
    "\n",
    "    if plot_likelihood:\n",
    "        # 似然分布 (两种写法等价)\n",
    "        # likelihood = pz.Beta(y,n-y)\n",
    "        # likelihood.plot_pdf(color=\"black\", ax=ax, legend=\"None\")\n",
    "        x = np.linspace(0,1,1000)\n",
    "        likelihood = pz.Binomial(n=n, p=y/n).pdf(x=x*n)\n",
    "        likelihood = likelihood * n\n",
    "        ax.plot(x, likelihood, color=\"black\", label=r\"$\\mathbf{Binomial}$\"+rf\"(n={n},p={round(y/n,2)})\")\n",
    "        ax.fill_between(x, likelihood, color=\"#0071b2\", alpha=0.5, label=\"likelihood\")\n",
    "\n",
    "    if plot_posterior:\n",
    "        # 后验分布\n",
    "        posterior = pz.Beta(alpha + y, beta + n - y)\n",
    "        posterior.plot_pdf(color=\"black\", ax=ax, legend=\"None\")\n",
    "        x_posterior = np.linspace(posterior.ppf(0.0001), posterior.ppf(0.9999), 100)\n",
    "        ax.fill_between(x_posterior, posterior.pdf(x_posterior), color=\"#009e74\", alpha=0.5, label=\"posterior\")\n",
    "\n",
    "    if show_legend:\n",
    "        ax.legend(loc=legend_loc)\n",
    "    else:\n",
    "        ax.legend().set_visible(False)\n",
    "\n",
    "    # 设置图形\n",
    "    ax.set_xlabel(xlabel)\n",
    "    sns.despine()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 创建一个单独的图和轴\n",
    "fig, ax = plt.subplots(figsize=(7, 5))\n",
    "\n",
    "# 先验参数 alpha=2, beta=2, 观测数据 y=9, n=10\n",
    "bayesian_analysis_plot(alpha=2, beta=2, y=9, n=10, ax=ax) \n",
    "\n",
    "# 显示图像\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "611A3F71379342B291B6606A90D48098",
    "jupyter": {},
    "notebookId": "654741f6d74b63fed5dd17ca",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "**选项b是更符合贝叶斯取向的回答**。 为什么？ ➡  \n",
    "\n",
    "* 我们来考虑另一种调查情况下得出的后验分布：  \n",
    "\n",
    "* 我们对$\\pi$的先验仍然为$\\pi \\sim Beta(2, 2)$，但现在我们的试验总次数为118次，成功次数为99次.  \n",
    "\n",
    "$$  \n",
    "\\pi \\sim Beta(2, 2)  \n",
    "$$  \n",
    "\n",
    "$$  \n",
    "Y | \\pi  \\sim Bin(118, \\pi)  \n",
    "$$  \n",
    "\n",
    "$$  \n",
    "\\pi | (y = 99) \\sim \\text{Beta}(\\alpha + y, \\beta + n - y)  \n",
    "$$  \n",
    "\n",
    "* 这种情况下，$\\pi$的后验分布满足$\\pi | (Y = 99) \\sim Beta(101, 21)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2F4AC71F465F4FF68EFFF0A6A1B17C48",
    "jupyter": {},
    "notebookId": "654741f6d74b63fed5dd17ca",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "下图展示了这两种情况下的后验分布  \n",
    "\n",
    "> 黑线表示众数，即在后验分布中最可能出现的值  \n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/sm3w84q11g.png?imageView2/0/w/700)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "* 在这两种分布下，$\\pi$最可能的取值都在83-84%左右  \n",
    "\n",
    "* 如果只关注众数，两种截然不同的情况却会导致相似的结论❌  \n",
    "\n",
    "* 但很明显，我们可以看到两图中$\\pi$的分布范围是不同的  \n",
    "\n",
    "\n",
    "**为了同时了解$\\pi$的集中趋势和离散趋势，我们可以使用 *95%的可信区间(credible intervals)* 来描述$\\pi$**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "B657AED2D8CC4619AB12A0E6535188EF",
    "jupyter": {},
    "notebookId": "654741f6d74b63fed5dd17ca",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### 可信区间(credible intervals)  \n",
    "\n",
    "* 后验分布的2.5%百分位数和97.5%百分位数包含的区域共同组成了95%的后验可信区间  \n",
    "\n",
    "* 可信区间表示了参数出现在这个区域的概率  \n",
    "    * 比如，Beta(101, 21) 95%的可信区间为(0.756, 0.889)。这意味着我们可以说，在随机点运动任务中参与者成功的真实概率出现在(0.756, 0.889)的可能性是95%  \n",
    "    * 一种理解是，有95%的人在随机点运动任务中参与者成功概率很高，大概为 0.756 到 0.889。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import beta\n",
    "\n",
    "# 定义 Beta 分布的参数 Beta(101, 21)\n",
    "params = [(11, 3), (101, 21)]\n",
    "titles = [r\"Beta(11, 3)\", r\"Beta(101, 21)\"]\n",
    "ci_level = 0.95\n",
    "\n",
    "# 创建图形和子图\n",
    "fig, axes = plt.subplots(1, 2, figsize=(8, 3), sharey=True)\n",
    "\n",
    "# 绘制 Beta 分布的 PDF 和 95% CI 区间\n",
    "for i, (a, b) in enumerate(params):\n",
    "    x = np.linspace(0, 1, 1000)\n",
    "    y = beta.pdf(x, a, b)\n",
    "    ci_lower, ci_upper = beta.ppf([(1 - ci_level) / 2, (1 + ci_level) / 2], a, b)\n",
    "    x2 = np.linspace(ci_lower, ci_upper, 1000)\n",
    "    y2 = beta.pdf(x2, a, b)\n",
    "\n",
    "    # 绘图\n",
    "    axes[i].plot(x, y, color='black', label=f'{int(ci_level*100)}% CI')\n",
    "    axes[i].fill_between(x2, y2, color='#a6bddb', alpha=0.6)\n",
    "    axes[i].set_title(titles[i])\n",
    "    axes[i].set_xlabel(r\"$\\pi$\")\n",
    "    axes[i].set_ylabel(\"density\")\n",
    "    axes[i].set_ylim(0, 12)  \n",
    "    \n",
    "    # 隐藏上部和右部的边框\n",
    "    axes[i].spines['top'].set_visible(False)\n",
    "    axes[i].spines['right'].set_visible(False)\n",
    "    \n",
    "    # 添加图例\n",
    "    axes[i].legend()\n",
    "\n",
    "# 调整子图布局\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "83A959A7A1CF46BB802021157CCDC4F6",
    "jupyter": {},
    "notebookId": "654741f6d74b63fed5dd17ca",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "**在报告可信区间时，95%是最常见的选项，但并不是唯一的选项。** \n",
    "\n",
    "* 我们也可以创建其他可信区间，比如Beta(101, 21)的分布之下：  \n",
    "\t* 50% 可信区间：由25%百分位数和75%百分位数包含的区域  \n",
    "\t* 99%可信区间：由0.5%百分位数和99.5%百分位数包含的区域  \n",
    "\n",
    "> 在95%CI的图中，由于后验分布是一个偏态分布，可以看到相较于前半部分，后半部分包含的值对应的概率更低。  \n",
    "> 当后验分布是偏态分布时，有时我们不以中位数为中心构建95%的可信区间，而是基于最高后验概率密度(众数)。  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x300 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import beta\n",
    "\n",
    "# 定义 Beta 分布的参数 Beta(101, 21)\n",
    "a, b = 101, 21\n",
    "x = np.linspace(0, 1, 1000)\n",
    "y = beta.pdf(x, a, b)\n",
    "\n",
    "# 设置三个不同的可信区间\n",
    "ci_levels = {\n",
    "    \"50% CI\": (0.25, 0.75),\n",
    "    \"95% CI\": (0.025, 0.975),\n",
    "    \"99% CI\": (0.005, 0.995)\n",
    "}\n",
    "ci_colors = ['#bdd7e7', '#6baed6', '#3182bd']  # Colors for 50%, 95%, and 99% CI\n",
    "\n",
    "# 为每个可信区间创建子图\n",
    "fig, axes = plt.subplots(1, 3, figsize=(12, 3), sharey=True)\n",
    "\n",
    "# 绘制每个可信区间\n",
    "for i, (ci_name, (lower_percentile, upper_percentile)) in enumerate(ci_levels.items()):\n",
    "    # 计算可信区间的上下界\n",
    "    ci_lower, ci_upper = beta.ppf([lower_percentile, upper_percentile], a, b)\n",
    "\n",
    "    # 绘制分布曲线并填充可信区间\n",
    "    axes[i].plot(x, y, color='black')\n",
    "    axes[i].fill_between(x, y, where=(x >= ci_lower) & (x <= ci_upper), color=ci_colors[i], alpha=0.6)\n",
    "    axes[i].set_title(f\"{ci_name} for Beta(101, 21)\")\n",
    "    axes[i].set_xlabel(r\"$\\pi$\")\n",
    "    axes[i].set_ylim(0, 12)\n",
    "    \n",
    "    # 绘制可信区间的垂直线\n",
    "    y_ci_lower = beta.pdf(ci_lower, a, b)\n",
    "    y_ci_upper = beta.pdf(ci_upper, a, b)\n",
    "    axes[i].axvline(ci_lower, color='black', linestyle='-', ymax=y_ci_lower / max(y))\n",
    "    axes[i].axvline(ci_upper, color='black', linestyle='-', ymax=y_ci_upper / max(y))\n",
    "    \n",
    "    # 移除顶部和右侧的边框\n",
    "    axes[i].spines['top'].set_visible(False)\n",
    "    axes[i].spines['right'].set_visible(False)\n",
    "\n",
    "    axes[i].set_xlim(0.5, 1)\n",
    "\n",
    "# 设置 y 轴标签\n",
    "axes[0].set_ylabel(\"density\")\n",
    "\n",
    "# 调整布局\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8810B449DD86450694CAFD3B16585D89",
    "jupyter": {},
    "notebookId": "654741f6d74b63fed5dd17ca",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "\n",
    "### 最大后验概率密度区间(the highest density interval, HDI)  \n",
    "\n",
    "最大概率密度区间HDI与中心区间是非常接近的。但是当后验分布为非正态分布时，两者存在区别，比如：  \n",
    "\n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/image/rjdef48vqj.png?imageView2/0/w/640/h/640)  \n",
    "\n",
    "- 此时，后验中心区间从中位数的两侧开始展开。  \n",
    "- 而最大概率密度区间HDI从y轴最高的两处开始展开。  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "EDB88893F6224F1F87098D4D96407509",
    "jupyter": {},
    "notebookId": "654741f6d74b63fed5dd17ca",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "直觉理解：想象有一根水平的线从后验概率密度最高点往下滑，如果是95%HDI，则意味着黄色部分的面积占曲线下面积的95%  \n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/s37y41n2yf.png?imageView2/0/w/640/h/640)  \n",
    "\n",
    "> source: https://mathematica.stackexchange.com/questions/173282/computing-credible-region-highest-posterior-density-from-empirical-distributio\n",
    "\n",
    "<div style=\"padding-bottom: 30px;\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "263E9234BAB94454B07769A13A768E85",
    "jupyter": {},
    "notebookId": "654741f6d74b63fed5dd17ca",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### 95% CI vs 95%HDI  \n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/s36vflrg1f.png?imageView2/0/w/960/h/960) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 总结  \n",
    "\n",
    "随着我们的贝叶斯模型越来越复杂，比如，一个回归模型加入越来越多的预测变量。\n",
    "\n",
    "这些模型的**后验将变得难以直接获得，或者无法获得**。  \n",
    "\n",
    "我们学习了在这种情况下逼近后验的两种模拟技术：  \n",
    "- 网格逼近和马尔科夫链蒙特卡罗。  \n",
    "- 两种技术都会产生 N 个 $\\Theta$ 参数值样本。注意，这里的 $\\Theta$  可能包含多个参数。  \n",
    "\n",
    "最后，我们学到了一些用于检查 MCMC 模拟质量的诊断方法。  \n",
    "- 可视化：直观地检查多个并行链的轨迹图和密度图，以确定模拟的稳定性和混合性。  \n",
    "- 数学指标：用有效样本量比、自相关性和 $\\hat{R}$等数值诊断来补充这些视觉诊断。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "此外，非正态分布后验的平均值，中位数和众数并不相等。  \n",
    "\n",
    "- 其中众数为分布最高点对应的参数值  \n",
    "- 中位数左右两侧分布的面积各占50%  \n",
    "- 平均值的位置接近中位数，并且它容易分布形态的影响  \n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/image/rjddhc2wo.png?imageView2/0/w/500/h/500)  \n",
    "\n",
    "> source: book--A Student’s Guide to Bayesian Statistics\n",
    "\n",
    "<div style=\"padding-bottom: 20px;\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7960A3C4240A4E38ADE0232CF93D9001",
    "jupyter": {},
    "notebookId": "654741f6d74b63fed5dd17ca",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Posterior hypothesis testing  \n",
    "\n",
    "后验推断能告诉我们 “反应的正确率为多少”的估计范围。\n",
    "\n",
    "但在传统的研究思路中，我们非常关心的是“正确率是否大于随机水平50%”（即虚无假设显著性检验），假如我们需要完成同样的推断，在贝叶斯框架下应该如何选择？\n",
    "\n",
    "* HDI + ROPE (最高密度区间 + 预设效应范围): 在贝叶斯分析中，HDI（Highest Density Interval）代表后验分布中概率最高的区间，而ROPE（Region of Practical Equivalence）则是一个预设的效果范围，用于判断效果是否具有实际意义。当HDI与ROPE重叠时，说明结果在实际应用中可能不显著；反之，则可能具有实际意义。\n",
    "\n",
    "\n",
    "> Heck, D. W., Boehm, U., Böing-Messing, F., Bürkner, P.-C., Derks, K., Dienes, Z., Fu, Q., Gu, X., Karimova, D., Kiers, H. A. L., Klugkist, I., Kuiper, R. M., Lee, M. D., Leenders, R., Leplaa, H. J., Linde, M., Ly, A., Meijerink-Bosman, M., Moerbeek, M., … Hoijtink, H. (2023). A review of applications of the bayes factor in psychological research. Psychological Methods, 28(3), 558–579. https://doi.org/10.1037/met0000454\n",
    "\n",
    "\n",
    "* Bayes Factor (贝叶斯因子): 贝叶斯因子是用于比较两种假设（通常是虚无假设与备择假设）相对支持程度的比率。它衡量的是数据在这两种假设下的解释能力。一个大于1的贝叶斯因子表示数据支持备择假设，而小于1则表示支持虚无假设。贝叶斯因子提供了一种量化不确定性的方法，能够帮助我们更好地理解结果的可靠性。\n",
    "\n",
    "\n",
    "> Kruschke, J. K. (2018). Rejecting or accepting parameter values in bayesian estimation. Advances in Methods and Practices in Psychological Science, 1(2), 270–280. https://doi.org/10.1177/2515245918771304"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    ">🤔假设我们在一篇报道中看到这样一种描述：在随机点运动任务中，成功次数占比为80%。 \n",
    "> 如何根据这个数据结果判断改成功率是否大于随机判断水平 50% 呢？  \n",
    "\n",
    "\n",
    "* 我们同时考虑两种可能性：成功次数 $\\pi$ 的比例是否与 50% 相同，此时备择假设和虚无假设可以写成：  \n",
    "$$  \n",
    "\\begin{split}  \n",
    "H_0: & \\; \\; \\pi = 0.5 \\\\  \n",
    "H_a: & \\; \\; \\pi \\ne 0.5 \\\\  \n",
    "\\end{split}  \n",
    "$$  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### 1. 通过 HDI 进行检验\n",
    "\n",
    "假设我们沿用之前的例子，并且已经知道先验分布为 $Beta(2, 2)$； 后验分布为 $Beta(101, 21)$。\n",
    "\n",
    "为了检验 $\\pi$ 是否显著不同于 0.5，我们可以计算 **后验分布的 HDI**（Highest Density Interval），这是一种包含后验分布中最高概率密度的区间。通常 HDI 表示一个区间，比如 95% HDI，意味着该区间包含了后验分布中的 95% 的概率质量。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**求解 HDI**\n",
    "\n",
    "HDI 是后验分布中包含最高密度的区间，我们通常计算 95% HDI，这意味着该区间包含后验分布中 95% 的概率质量。HDI 的定义要求该区间 $[\\pi_\\text{low}, \\pi_\\text{high}]$ 满足以下条件：\n",
    "\n",
    "1. 对于任何 $\\pi$ 在区间 $[\\pi_\\text{low}, \\pi_\\text{high}]$ 外的点，它的密度都小于区间内的点的密度，即：\n",
    "\n",
    "$$f(\\pi_\\text{low} | \\alpha, \\beta) = f(\\pi_\\text{high} | \\alpha, \\beta)$$\n",
    "\n",
    "1. 该区间内的概率质量为 95%：\n",
    "\n",
    "$$\\int_{\\pi_\\text{low}}^{\\pi_\\text{high}} f(\\pi | \\alpha, \\beta) d\\pi = 0.95$$\n",
    "\n",
    "Arviz 提供计算 HDI 的方法 `arviz.summary`，通过这种方法，我们可以计算出后验分布 $Beta(101, 21)$ 的 95% HDI 区间。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**结果解释**\n",
    "\n",
    "经过计算，得到的 95% HDI 区间为 $[0.76, 0.89]$。接下来，我们要验证这个区间是否包含 0.5：\n",
    "\n",
    "- 该区间为 $[0.76, 0.89]$。\n",
    "- 0.5 不在这个区间内。\n",
    "\n",
    "因此，95% HDI 区间不包含 0.5，这表明在 95% 的可信水平下，成功率 $\\pi$ 与 0.5 存在显著差异。基于这一结果，我们可以拒绝虚无假设 $H_0: \\pi = 0.5$，并认为成功率 $\\pi$ 显著不同于 0.5。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import arviz as az\n",
    "import scipy.stats as stats\n",
    "\n",
    "# 生成 Beta 分布的样本\n",
    "alpha = 101\n",
    "beta = 21\n",
    "samples = np.random.beta(alpha, beta, 10000)\n",
    "\n",
    "# 使用 arviz 绘制后验分布图\n",
    "az.plot_posterior(samples, hdi_prob=0.95)\n",
    "\n",
    "# 添加 x=0.5的竖线\n",
    "plt.axvline(x=0.5, color='red', linestyle='--')\n",
    "\n",
    "# 显示图形\n",
    "plt.show() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. 通过 HDI + ROPE 进行检验\n",
    "\n",
    "**ROPE**（Region of Practical Equivalence，实际等效区间）是一种贝叶斯统计中的概念，用来定义在实践中认为与虚无假设无显著差异的区域。通过结合 HDI 和 ROPE，我们可以进一步检验成功率 $\\pi$ 是否在实践中显著不同于 0.5。\n",
    "\n",
    "\n",
    "在这个例子中，我们假设 ROPE 的范围为 $[0.4, 0.6]$。这意味着如果成功率 $\\pi$ 落入这个区间，我们认为 $\\pi$ 在实践中与随机判断水平 0.5 没有显著差异。因此，我们的目标是判断 95% HDI 区间是否完全落在 ROPE 内，完全在 ROPE 外，或者部分重合。\n",
    "\n",
    "> 注意：ROPE需要我们根据具体情况进行调整。 一般情况下需要参考经验值或文献中的建议。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**检验步骤**\n",
    "\n",
    "\n",
    "我们已经知道 95% HDI 区间为 $[0.76, 0.89]$。接下来，我们需要将这个区间与 ROPE 区间 $[0.4, 0.6]$ 进行比较：\n",
    "\n",
    "- HDI 区间为 $[0.76, 0.89]$。\n",
    "- ROPE 区间为 $[0.4, 0.6]$。\n",
    "\n",
    "接下来，我们考虑三种可能的情况：\n",
    "\n",
    "- **HDI 完全落在 ROPE 之内**：如果 95% HDI 完全在 $[0.4, 0.6]$ 之内，那么可以认为 $\\pi$ 在实践中与 0.5 无显著差异。\n",
    "- **HDI 完全落在 ROPE 之外**：如果 95% HDI 完全在 $[0.4, 0.6]$ 之外，那么可以认为 $\\pi$ 在实践中显著不同于 0.5。\n",
    "- **HDI 与 ROPE 部分重合**：如果 95% HDI 区间与 ROPE 有部分重合，那么可以认为不确定 $\\pi$ 是否显著不同于 0.5。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**结果分析**\n",
    "\n",
    "在我们的例子中，HDI 区间 $[0.76, 0.89]$ 完全位于 ROPE 区间 $[0.4, 0.6]$ 之外。这意味着我们可以认为 $\\pi$ 在实践中与 0.5 存在显著差异，且成功率 $\\pi$ 显著高于 50%。\n",
    "\n",
    "HDI 区间 $[0.76, 0.89]$ 完全落在 ROPE 之外，这表明成功率 $\\pi$ 在实践中显著不同于随机判断水平 0.5。结合 HDI 和 ROPE 的结果，我们可以进一步确认成功率 $\\pi$ 显著高于 0.5。\n",
    "\n",
    "因此，基于 HDI + ROPE 的检验结果，我们可以认为成功率 $\\pi$ 不仅在统计学上（通过 HDI 检验），而且在实践中（通过 ROPE 检验）都显著不同于 50%。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import arviz as az\n",
    "\n",
    "# 生成 Beta 分布的样本\n",
    "alpha = 101\n",
    "beta = 21\n",
    "samples = np.random.beta(alpha, beta, 10000)\n",
    "\n",
    "# 使用 arviz 绘制后验分布图，并添加 ROPE 区间\n",
    "az.plot_posterior(samples, hdi_prob=0.95, rope=[0.4, 0.6])\n",
    "\n",
    "# 显示图形\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 贝叶斯因子(Bayes Factor, BF)  \n",
    "\n",
    "贝叶斯因子是用于比较两种假设（通常是虚无假设和备择假设）相对支持程度的一个量化工具。它通过计算在两种假设下观察到的数据的概率，来评估这些假设的相对可信度。\n",
    "\n",
    "从先验到后验，**数据**让备择假设的相对可能性发生了改变。  \n",
    "\n",
    "我们可以使用**贝叶斯因子**来量化**数据**对我们信念更新的程度：  \n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\text{Bayes Factor} &= \\frac{\\text{posterior odds }}{\\text{prior odds }} \\\\\n",
    "&= \\frac{\\text{后验概率比}}{\\text{先验概率比}}  \\\\\n",
    "&= \\frac{P(H_a | Y) / P(H_0 | Y)}{P(H_a) / P(H_0)}  \n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "\n",
    "* $BF_{a0}$ = 1，收集到的数据并没有改变备择假设$H_a$的相对可能性  \n",
    "* $BF_{a0}$ > 1，收集到的数据增加了备择假设$H_a$的相对可能性。BF越大，表明支持备择假设$H_a$的证据越强  \n",
    "* $BF_{a0}$ < 1，收集到的数据削弱了备择假设$H_a$的相对可能性。BF越小，表明支持备择假设$H_a$的证据越弱  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "|**贝叶斯因子** |**解读**|  \n",
    "|-|-|  \n",
    "|> 100|极强的证据支持$H_a$|  \n",
    "|30 ~ 100|非常强的证据支持$H_a$|  \n",
    "|10 ~ 30|较强的证据支持$H_a$|  \n",
    "|3 ~ 10|中等程度的证据支持$H_a$|  \n",
    "|1 ~ 3|较弱的证据支持$H_a$|  \n",
    "|1|没有证据|  \n",
    "|1/3 ~ 1|较弱的证据支持$H_0$|  \n",
    "|1/10 ~ 1/3|中等程度的证据支持$H_0$|  \n",
    "|1/30 ~ 1/10|较强的证据支持$H_0$|  \n",
    "|1/100 ~ 1/30|非常强的证据支持$H_0$|  \n",
    "|< 1/100|极强的证据支持$H_0$|  \n",
    "\n",
    "> Source: 该表改编自胡传鹏等(2018)，源引用于Lee & Wagenmakers (2014)。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. 通过贝叶斯因子 (Bayes Factor, BF) 进行检验\n",
    "\n",
    "回到之前的例子，我们已知$\\pi = 0.8$是成功事件发生的概率，先验分布为 $Beta(2, 2)$； 后验分布为 $Beta(101, 21)$。\n",
    "\n",
    "\n",
    "* 但此时我们会遇到一个问题，因为$\\pi$的后验分布是连续的，对于连续型变量，单个值发生的概率为0(一条线)：  \n",
    "$$  \n",
    "P(\\pi = 0.8 | Y) = \\int_{0.8}^{0.8} f(\\pi | y)d\\pi = 0  \n",
    "$$  \n",
    "\n",
    "* 那么备择假设发生的概率为：  \n",
    "$$  \n",
    "P(\\pi \\ne 0.8 | Y) = 1 - P(\\pi = 0.8 | Y) = 1  \n",
    "$$  \n",
    "\n",
    "* 此时如果我们仍然沿用刚刚的公式计算后验概率比：  \n",
    "$$  \n",
    "\\text{Posterior odds } = \\frac{P(H_a \\; | \\; Y)}{P(H_0 \\; | \\; Y)} = \\frac{1}{0} = \\text{ nooooo!}  \n",
    "$$  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "既然在连续型变量中，考虑单个值的概率会遇到计算上的问题，我们需要引入**区间**来计算贝叶斯因子，比如使用 ROPE 的范围，检验成功次数比例$\\pi$是否在(0.4, 0.6)这个区间内：  \n",
    "\n",
    "$$  \n",
    "\\begin{split}  \n",
    "H_0: & \\; \\; \\pi \\in (0.4, 0.6) \\\\  \n",
    "H_a: & \\; \\; \\pi \\notin (0.4, 0.6) \\\\  \n",
    "\\end{split}  \n",
    "$$  \n",
    "\n",
    "**贝叶斯因子假设检验公式**\n",
    "\n",
    "$$\n",
    "BF = \\frac{P(H0|Y)/P(H0)}{P(H1|Y)/P(H0)}\n",
    "$$\n",
    "\n",
    "* 注意：我们需要为 H0 和 H1 设置先验概率，这里我们假设两者出现的概率为 0.5, $P(H0) = 0.5$, $P(H1) = 0.5$。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "**贝叶斯因子的计算**\n",
    "\n",
    "\n",
    "首先，我们需要确定 $\\pi$ 在 ROPE 范围 $(0.4, 0.6)$ 内的概率，即：\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "P(H0|Y) &= P(0.4 \\leq \\pi \\leq 0.6 | Y) = \\int_{0.4}^{0.6} f(\\pi | Y) d\\pi \\\\\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "- 其中 $f(\\pi | Y)$ 是 $\\pi$ 的后验密度函数。根据我们的后验分布 $Beta(101, 21)$，我们可以使用积分或数值方法来求解具体数值。\n",
    "\n",
    "与此同时，我们考虑 $(0.4, 0.6)$ 之外的概率，即 $P(\\pi \\notin (0.4, 0.6) | Y)$，通过：\n",
    "\n",
    "$$\n",
    "P(H1|Y) = P(\\pi \\notin (0.4, 0.6) | Y) = 1 - P(H0|Y)\n",
    "$$\n",
    "\n",
    "现在我们可以根据下式计算贝叶斯因子（BF）：\n",
    "\n",
    "$$\n",
    "\\text{Bayes Factor } = \\frac{P(0.4 \\leq \\pi \\leq 0.6 | Y)/P(H0)}{P(\\pi \\notin (0.4, 0.6) | Y)/P(H1)}\n",
    "$$\n",
    "\n",
    "**由于两种假设下先验分布相同，$P(H0) = P(H1) = 0.5$，因此可以简化计算为：**\n",
    "\n",
    "$$\n",
    "\\text{Bayes Factor } = \\frac{P(0.4 \\leq \\pi \\leq 0.6 | Y)}{P(\\pi \\notin (0.4, 0.6) | Y)}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**结果分析**\n",
    "\n",
    "\n",
    "计算 $P(0.4 \\leq \\pi \\leq 0.6 | Y)$ 可以用贝塔分布的累积分布函数（CDF）进行:\n",
    "\n",
    "$$P(0.4 \\leq \\pi \\leq 0.6 | Y) = F(0.6) - F(0.4)$$\n",
    "\n",
    "- 其中 $F$ 是以$ Beta$ 分布(101,21)累积分布函数。则，\n",
    "\n",
    "$$P(0.4 \\leq \\pi \\leq 0.6 | Y) \\approx 0.022 - 0.0003 = 0.0217$$\n",
    "\n",
    "因此，$P(\\pi \\notin (0.4, 0.6) | Y) = 1 - 0.0217 = 0.9783$。\n",
    "\n",
    "计算贝叶斯因子（BF）:\n",
    "$$\\text{Bayes Factor} = \\frac{P(0.4 \\leq \\pi \\leq 0.6 | Y)}{P(\\pi \\notin (0.4, 0.6) | Y)} \\approx \\frac{0.0217}{0.9783} \\approx 0.0222$$\n",
    "\n",
    "贝叶斯因子的值约为 $0.0222$，这意味着备择假设 $H_a$ ($\\pi$ 不在 $(0.4, 0.6)$ 区间内) 相对于原假设 $H_0$ ($\\pi$ 在 $(0.4, 0.6)$ 区间内) 获得了极大的支持。这个结果表明，给定数据和先验信息，$\\pi$ 值显著不在 $(0.4, 0.6)$ 区间内，大大倾向于 $\\pi$ 的真实值远离 $0.5$，这与 $\\pi = 0.8$ 的假设一致。\n",
    "\n",
    "因此，我们可以结论认为，在给定的统计模型和数据条件下，成功率 $\\pi = 0.8$ 是显著高于一般随机判断水平（$0.5$），这进一步强化了 $\\pi$ 显著高于 $0.5$ 的结论。此结果对于决策支持和进一步的统计分析具有重要意义。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**额外补充：单侧检验**  \n",
    "\n",
    "贝叶斯后验模型可以直接进行单侧检验，例如要检验成功率小于80%的假设，我们只需要计算后验分布中$\\pi$小于80%的概率即可。  \n",
    "\n",
    "* 那么，我们可以考虑在后验分布$Beta(101，21)$中，$\\pi$小于0.8的概率  \n",
    "$$  \n",
    "P(\\pi < 0.8 \\; | \\; Y = 99) = \\int_{0}^{0.8}f(\\pi | y=99)d\\pi .  \n",
    "$$  \n",
    "\n",
    "(如图，可以理解为$\\pi$从0 ~ 0.8围成的曲线下面积)  \n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/sm3ylkxvv1.png?imageView2/0/w/720/h/960)\n",
    "\n",
    "经计算可知，在$Beta(101, 21)$中，$\\pi$小于0.8的概率是20.2%\n",
    "\n",
    "\n",
    "<div style=\"padding-bottom: 30px;\"></div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**单侧检验--假设检验**\n",
    "\n",
    "如果我们把这个问题放到假设检验的框架下，那么这个问题可以写成：  \n",
    "\n",
    "* 虚无假设 ($H_0$)：在随机点运动任务中，成功次数占比等于0.8（即80%）\n",
    "* 备择假设 ($H_1$)：在随机点运动任务中，成功次数占比大于0.8（即80%）\n",
    "\n",
    "$$  \n",
    "\\begin{split}  \n",
    "H_0: & \\; \\; \\pi \\ge 0.8 \\\\  \n",
    "H_a: & \\; \\; \\pi < 0.8 \\\\  \n",
    "\\end{split}  \n",
    "$$  \n",
    "\n",
    "我们可以计算出这两个假设对应的后验概率：  \n",
    "\n",
    "* 备择假设：$\\pi < 0.8$  \n",
    "$$  \n",
    "P(H_a \\; | \\; Y=99) = 0.202  \n",
    "$$  \n",
    "\n",
    "* 虚无假设：$\\pi \\ge 0.8$  \n",
    "$$  \n",
    "P(H_0 \\; | \\; Y=99) = 1-P(H_a \\; | \\; Y=99) = 0.798\n",
    "$$  \n",
    "\n",
    "将这二者相除，我们可以知道备择假设发生的可能性大约是虚无假设的3倍，这被称为**后验概率比(posterior odds)**  \n",
    "\n",
    "$$  \n",
    "\\text{posterior odds } = \\frac{P(H_a \\; | \\; Y=99)}{P(H_0 \\; | \\; Y=99)} \\approx 0.253.  \n",
    "$$  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们说$\\pi$的后验概率表现了对$\\pi$信念在数据与先验之间的平均更新，那么我们可以看一下在**先验分布** $Beta(2,2)$ 中，虚无假设和备择假设发生的可能性  \n",
    "\n",
    "* 备择假设：$\\pi < 0.8$  \n",
    "$$  \n",
    "P(H_a) = \\int_0^{0.8} f(\\pi) d\\pi \\approx 0.8  \n",
    "$$  \n",
    "\n",
    "* 虚无假设：$\\pi \\ge 0.8$  \n",
    "$$  \n",
    "P(H_0) = 1-P(H_a) \\approx 0.2 \n",
    "$$  \n",
    "\n",
    "* 先验概率比：  \n",
    "$$  \n",
    "\\text{Prior odds } = \\frac{P(H_a)}{P(H_0)} \\approx 4\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "> $$  \n",
    "> \\text{posterior odds } \\approx 0.253\n",
    "> $$  \n",
    "> $$  \n",
    "> \\text{Prior odds } \\approx 4  \n",
    "> $$  \n",
    "\n",
    "从先验到后验，**数据**让备择假设的相对可能性发生了改变。  \n",
    "\n",
    "我们可以使用**贝叶斯因子**来量化**数据**对我们信念更新的程度：  \n",
    "\n",
    "$$  \n",
    "\\text{Bayes Factor} = \\frac{\\text{posterior odds }}{\\text{prior odds }} = \\frac{\\text{后验概率比}}{\\text{先验概率比}}  \n",
    "$$  \n",
    "\n",
    "代入我们的数据中  \n",
    "$$  \n",
    "\\text{Bayes Factor} = \\frac{0.253}{4} \\approx 0.063\n",
    "$$  \n",
    "\n",
    "* 在这个例子中，贝叶斯因子大约是0.063，这表明，数据对虚无假设的支持度实际上是大于备择假设的，相比先验分布，数据使得备择假设相对虚无假设的支持度下降了。\n",
    "\n",
    "\n",
    "综上，后验概率 $P(H_a \\; | \\; Y=99) = 0.202$  表示数据对备择假设$H_a$ 的支持度是20.2%，反映出数据并未提供有力证据来支持成功率低于 80% 的假设。这与频率主义统计方法的决策机制不同：\n",
    "\n",
    "* 不同于我们曾经在频率主义框架下所做的那样：根据*p*值的大小拒绝或无法拒绝零假设。  \n",
    "\n",
    "* 在贝叶斯学派中，不提倡一刀切标准。数据可以告诉我们后验概率或贝叶斯因子，从而告诉我们证据有多**强**。它只是衡量不同的假设发生的相对可能性。\n",
    "\n",
    "\n",
    "<div style=\"padding-bottom: 30px;\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6212227DC427499FA70A11B047466F8A",
    "jupyter": {},
    "notebookId": "654741f6d74b63fed5dd17ca",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Summary and discussion  \n",
    "\n",
    "<p align=\"center\">\n",
    "  <img src=\"https://cdn.kesci.com/upload/sm7veon5ei.png?imageView2/0/w/720/h/960\" alt=\"Image Name\">\n",
    "</p>\n",
    "\n",
    "本节课我们学习了如何利用精确或近似的后验模型，对未知参数进行统计分析，包括：  \n",
    "1. 后验预测(均值和可信区间)  \n",
    "2. 基于后验的假设检验  \n",
    "3. 后验预测  \n",
    "\n",
    "😎到这里你或许发现了贝叶斯的独特之处，相比于之前学习的基于频率学派(frequentists)的统计方法。\n",
    "\n",
    "<div style=\"padding-bottom: 20px;\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "35DD3915771542B0B2F013F3B2BE200A",
    "jupyter": {},
    "notebookId": "654741f6d74b63fed5dd17ca",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "贝叶斯分析结果的易解释性 -- 样本和总体的关系  \n",
    "\n",
    "- 贝叶斯分析根据观察到的数据 Y 来评估未知参数 π 的不确定性。  \n",
    "    \n",
    "    - 例如，在随机点运动任务中，有 118 次尝试，其中 99 次成功完成任务。\n",
    "    - 根据这一观察结果，我们确定在随机点运动任务中成功完成的比例 π 低于 0.80 的后验概率为 20.2%  \n",
    "        \n",
    "- 在频数分析中，往往根据对于总体性质π的假定值来评估观测样本Y的不确定性。  \n",
    "    \n",
    "    - 频率学派假设只要无限(long-run)的进行抽样，样本分布的参数就会近似总体分布。  \n",
    "    - 然后，根据零假设显著性检验(Null Hypothesis Significance Testing)和 p 值来判断样本和总体的关系。  \n",
    "    - 例如，频率学派假设 π 为 0.80时，我们观察到的样本(118 次尝试)中，有 Y = 99 次的成功次数，那么这一结果可能会被视为样本与总体的差异。\n",
    "        \n",
    "\n",
    "假设检验的哲学基础是波普尔的科学可证伪性  \n",
    "  - 它所回答的问题对人脑来说却**不那么自然**：因为我们实际上观察到了数据，但却不知道π，所以要解释一个假设相反的计算结果，可能会让人费解。  \n",
    "  - 然而，在检验假设时，更自然的做法是问 \"我的假设有多大可能性？(贝叶斯概率的答案），\n",
    "  - 而不是 \"如果我的假设不成立，我的数据的可能性有多大？(频繁概率的答案）。  \n",
    "  - 鉴于P值经常被曲解，进而被误用，整个频繁主义和贝叶斯理论都越来越不强调P值。"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "pymc5_3.11",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
